Meet The Legendary Creator of Famous Daredevil Foe Typhoid Mary | Women of Marvel

[MUSIC PLAYING] Hey, guys.
I’m Judy. And I’m Sana. And we’re here from
the Women of Marvel. And we are back with a special
80th anniversary episode, and we’re excited to be
joined by Ann Nocenti. Hi. Hello. We’re so excited
to have Ann here. Ann is a very well known
editor, writer, filmmaker. You’ve done so much
across the board. But you’re such a
big part of Marvel’s history, the legacy of Marvel
in the ’80s in particular. And there was one
character, which is a personal favorite
of mine, that you created named Typhoid Mary. Uh oh. That is exactly
what you should say. What’s she doing in the room? Tell us about Typhoid
Mary and how she came to be. ANN NOCENTI: Well,
I think that a hero is only as good as its villain. When John Romita, Jr., and
I were working on Daredevil, we wanted to give Daredevil
a really good villain. He had a couple personalities. You know, he was a
lawyer and a vigilante, so if he didn’t solve
it in the courts, he solved it in the streets. He wore a devil suit. He was a lapsed Catholic. We felt like he was
full of contradictions, so give him a female that
had a lot of different sides. And so we created a
character where there would be an innocent Mary
who would seduce Matt Murdock, while
the wild Typhoid would seduce Daredevil’s darker side. It’s comics. Hey, you can have
lots of personalities. You already have an ego and
an alter ego and a mask. Why not have, like, five more? The conversation that we
had with you on the podcast really showcased all of
your different personalities as well, some of the darker side
of Ann Nocenti, which you guys should definitely check
out because there’s a great conversation. We learned a lot more about
the history of Marvel, all of the amazing things
Ann is doing right now. So Ann, thanks for joining us. And you guys, go check it out. This is Marvel. Your universe. Thank you. [MUSIC PLAYING]

Four Words for Any Family Crisis

Kate (reading question from viewer): “My mother has had a medical emergency. And I’ll be flying out to see her with the rest my family. How does one be supportive in these instances while not buying into the fear that no doubt will be running rampant through my family?” “Talking truth (as I understand it currently) would be seen as callous and hurtful and fall into the category of pearls before swine (in biblical terms).” “I know I’m not responsible for others’ thoughts. But I feel compassion for them and would like to ease their suffering if I’m able to.” GF: Two things quickly. Number one. You’re right, don’t you dare go in there as a messiah — you know, teaching everybody how they should use the moment (and all the rest of that). That is, unless you don’t want to have to give gifts anymore. Audience: laughs. GF: I’ll let you think about it. On the other hand, here’s a simple phrase that applies to all situations like this. And I wish I thought of it a long time ago. You might want to write it down. “Bear All and Follow None.” “Bear All and Follow None.” What does that mean? I’m going go in there. And I am going to be the one who (instead of being carried away by the fear, the grief, the worry), I’m going to BEAR ALL of it consciously. I will receive it, as the lake should the nut. And I will allow the lake to return to its natural state–which by its presence will comfort everyone and everything around it. Because you’re not a part of the agitation. (That’s the “Bear All”.) “Follow None” means that you don’t become like the nut that falls into the pond. You don’t become caught up in all the thoughts and feelings going on around you (or going on within you) about the familial situation. “Bear All and Follow None.” Four words for any family crisis.

The Strangest Secret by Earl Nightingale (Law of Attraction)

I but to tell you about the strangest
secret in the world the secret some years ago the late Nobel
prize-winning doctor albert schweitzer was being interviewed in london is a
reporter asked him doctor what’s wrong with me and today
the radar to reserve a moment too many said the secret him simply don’t think it’s about this that I want to talk with you we have
today in a golden age this is a mirror that man is look forward to dream go to
work toward for thousands of years but since it’s here we pretty well take
it for granted we’ve America Europe particularly fortunate to live in a rich
history and that ever existed on the face of the earth forever but England opportunity for
everyone but you know what happens were 600
Minister even at the age of 24 I do you have any
idea what will happen to those men with bitterness sixty-third these 100 menu all-star even that the
225 believe they’re going to be successful the secret if you ask really what are these really
wanted to be a success he did he did you notice it he was eager toward life
that there was a certain the secret sparkle in his eye any witness to risk a
region life seemed like a pretty interesting adventure touring but by the time they’re 65 one will be rich 4 will be financially
independent 5 will still be working 54 will be broke take a moment out of the
100 only five make the grade know why do so many 30 what has happened
to the sparkle it was there when they were twenty bride what’s become a big dreams I hope so
plans and why is there such a large disparity between what these men
intended to do in what they actually accomplished when
we see about 5 percent achieve success we have to define success and here’s the best definition I’ve
never been able to find success is the progressive realization bubble
with the ideal if a man is working toward a
pre-determined goal and knows where he’s going that man is a success if he’s not doing that he’s a failure
success is the progress in realization bub on worthy ideal Romay the
distinguished psychiatrist wrote a wonderful book called man’s search for himself and in this
book he says the opposite of courage in our society
is not cowardice it is conformity in there you have the
trouble today its conformity people acting like
everyone else without knowing why without knowing where they’re going I think a bit in America right now
they’re over 8 p.m. million people 65 years of age
and older the secret in most urban are broke they’re
dependent the secret on someone else for life mississippi’s
elementary but the time was serving with him to make a living but a 225 usually
but at a time when are we making a living or supporting a family and the above the game were 65 we have
learned how to become financially independent in the richest way and that has never
been known way we can form a and the trouble is a
working with the wrong person which group they may be right who don’t
succeed why do these people conform where we
really don’t know these people believe that there was a
shipper circumstances but things that happened to them but
exterior forces fear outer directed people a survey was made
one time that covered a lot of men working in these men were asked where do
you work when you get up in the morning 1920 had no idea if US criminal 0 everyone goes to work in the morning ms
the reason they do it because everyone else is doing it but was your back to a definition of
success who succeeds the only person who succeeds is the
person who is progressively we are rising a worthy ideal is a person who says I’m going to become this ’em then begins
to work toward that goal I’ll tell you the successful people are
their success is the school teachers teaching school because that’s where he
or she wants to do the success is the woman is
away from mother because she wanted to become a working mother the secret is doing a good job of it this success
is a man who runs the corner gas station because that was his dream that’s what
he wanted to do the success is the successful salesman
who want to become a top much sales would grow and build his organization his successes everyone who is doing
deliberately a pre-determined job because that’s what
he decided to do deliberately but only 10 to 20 years
with that’s why today there isn’t really any competition unless we
make it for z/os instead of competing all we have to do
is create in over 20 years over to the key
which would determine what would happen to a human being was there a key I wanted to know which
would make the future a promise that we could foretell to a large extent was Ricky that would guarantee a
person’s becoming successful if you only knew about it then you how to use it well there is
such a key and I found it have you ever wondered why so many men
work so hard upon the Sri without ever achieving anything in particular and others don’t seem to work already
yes seem to get everything they seem to have it Meggie church you
produce it at about seven everything he touches turns to gold did you ever noticed a man to become
successful teams to continue to become successful and on the other hand you know to store
manager failure games to continue to fail well it’s because I’m goals Somerset
goals john told people with goals succeed
because they know where they’re going the secret it’s that simple thank you for Shipley
the harbor and take it with a complete origin and getting blamed captivity crude or reject the words or
you know how long it’ll take it has a definite go than 9,999 times
out of ten thousand it will get to where it started out to
get by mistake a membership just like a first only does not put a
crew under chapter for whom rescue but no im in point no gold
restoration we just start the engine let it go I think you’ll agree with me that if it
gets into the harbor of the readers single wind up on some
deserted beach a better look it can’t go any place because it has no
destination node Aidens it was the same with a human being take
a salesman for example there’s no other person in the world
today with the future have a good salesman showing is the world’s highest-paid
profession if we’re good at it and if we know where we’re going every
company needs to not salesman and the reward those men
the sky’s the limit for them but how many can you find someone once
said the human race is fixed not to prevent the strong women but to
prevent the week from using the American economy today
can be likened to a convoy NK before the entire economy is slow down to
protect its weakest link just as the convoy had to go to speed it
would reduce your stress or email information that’s why it’s so easy to make a living
today it takes no particular brains are trying to make a living a supportive
family to rate so we have a platter also call security
official rivers is looking for but we do have to decide how hi above
this plateau we want to wait dollars get back to the strangest secret
in the world a story that I wanted to tell you today when two men with goals succeed in life
and then without them for you well let me tell you something which if
you really understand it will alter your life immediately if you understand completely
what I’m going to tell you from this moment on your life will never be the
same again you suddenly find it good luck there
seems to be a jerk to do the things you want just seemed fall in
line informality whatever problems the worries it knowing all the buildings are a beer
perhaps you’ve experienced before doubt fear will be things in the past is the key to success and the key to
failure we become what we think about let me say that again we become what we think about through a little
history the grade wise men and teachers philosophers and profits have disagreed
with one another on many different things is only on this one point that they’re
incomplete n unanimous agreement was lowered Marcus
Aurelius Rodrigo membership a man’s life is what his thoughts make
it israelis are theirs everything comes over me and will only
wait I brought my sober long meditation to the conviction that a human being
would assert our purpose you must accomplish it and that nothing can resist a will that
will stick even existence for its fulfilment Ralph Waldo Emerson
sugars a man is what he thinks about all day
long the secret William James said the greatest
discovery of my generation is that human beings can alter their own
iris by altering their attributes but my end
he also said we need only in cold blood at as if the
thing in question worry your and it will become infallibly real by
growing into such a connection with her life that it will become real it will become
so Nick with Habitat the motion that are interest in it will be those
which characterize belief the also said if you only care about it
for a result you almost certainly appeal it if you
wish to be rich he will be rich if you wish to be heard
you will be alerted if you wish to be good you’ll be good
only you must in really wish these things in which the exclusively not we should be seen going together
incompatible things just as strongly in the Bible you read more at 9:23 is
okay just for you all things are possible to him that
believeth well-protected Norman Vincent Peale put
it this way this is one of the greatest floors in
the universe fervently do I wish I discovered it as a very young man it dawned upon me much later in life an
iPhone to be one of the greatest is not my greatest discovery outside my
relationship to God the great blog reveals simply stated is
that if you think in negative terms you will get negative
results if you think in positive terms you will
achieve positive results that is a simple fact he went on to say
which is at the bases astonishing law prosperity and success in three words believe them succeed William Shakespeare but it is wat are
doubts are traitors and make us lose the good we oft might win by fearing to
attempt George Bernard Shaw said people are
always bringing their circumstances will appear I don’t believe in circumstances the
people get on in this world to people get a new look for the circumstances
they want and if they can find them make him where
is pretty apparent is it and every person to discover this for a
while believe that he was the first one to work it out we become what we think about it stands to reason that a person is
thinking about a concrete in worthwhile goal is going to reach you because that’s what he’s thinking about
and we become what we think about commercially the man who has no goal
doesn’t know where he’s going and who saw she was there will be tortured
confusion anxiety and fear and worry because what he thinks about his life
becomes wanna frustration and fear and anxiety worry if he thinks about nothing he becomes
nothing but how does it work why do we become
what we think about well I’ll tell you how it works as far
as we know reading this I want to tell you about a situation that
parallels the human mind suppose a farmer has some weight and
it’s good for two layered by the way and gives performance choice the secret here April in that way and whatever he
chooses go and doesn’t care is a performer to make the decision
remember working during the human mind with the way and because the money right
away and doesn’t care what you put into it it
will return what you paid that he doesn’t care what you prayed
members say that the former has two seats in the same wanna see the corn the others make sure
to deadly poison he digs to hold a mere three players
both 321 corn the other night should it was a bit cold
waters and a share the land and what will happen invariably the rain
returned which pointed he’d written in the Bible as you sow
share you reap they remember their rendition care
return poisoning just really wonderful abundance as we reported short term the two groups one corn one
poison for human mind is far more fertile for
more incredible a mysterious some more rain but it works the same way it doesn’t care what we proved Sixers
failure the concrete with where we’re going for
confusion misunderstanding feared anxiety is
showing but what we planned it must returned to
us is he the human mind is the last great
explored culturally orders it contained riches beyond our
wildest dreams it will return anything we want to point there you might say work that’s true I
don’t people use their minds more when I think that figure is a great way
to mine comes as standard equipment at birth is free and things will be given
was for nothing replaces there you are things that we pay money
for we dare you the paradox is that exactly the reverse
is true everything we’ve really worth when we
might Cambridge free merger soldier bodies our hopes our
dreams our ambitions are intelligence are you have a family and children
crimson country all these priceless possessions free the secret but the things that cost us money are
actually very cheap and to be replaced at any time a good man can be completely wiped out
to make another fortune you can be there several times even over home burned down we can
rebuild it but the things we good for nothing we can never replace the human mind is
in use because we take it for granted familiarity breeds contempt it could do
it he got a job we certainly do it but generally speaking we use it for a
little jobs is terribly important universities approve it most was your
operating at about 10 percent for racial abilities to decide no what is it you want print your goal in your mind it’s the
most important decision you ever make in your entire life what is it you want you want to be an outstanding salesman a
better worker at your particular job you want to go places near complete in
your community you want to get rich all you gotta do is plant that seed in
your mind care for it work steadily toward your
goal they will become a reality it not only
will there’s no way that it cannot is the that’s a law like the larger Sir Isaac
Newton’s laws of gravity if you get on capitol building a jump of you always go
down you never go up it’s the same with all the other laws a major they always work their inflexible think
about your goal relaxed positive way it yourself in your minds
are as having already achieved this goal see yourself doing the things you will
be doing when you reach your goal president goalie feet above the doorway
GTG ulcers are you nervous breakdowns you can call raisers at a time when medical research is
racist when you put it to good health and longevity far too many others were
your shows it would be really great credit cope with things in our own little
personal ways without doing a few great laws will take
care of everything for us these things we bring on our sales to
our a bitch your way of thinking every one of us is the sum total his own
thoughtsthe secret he is where he is because that’s exactly
where he really wants to be whether you admit they remove each of us must really well for free to
this starts in the future because what you think today tomorrow
next month the next year will mold your life and determine your
future your guided by your mind I remember when
I was driving through eastern Arizona May so when I was picturing a person
moving machines roaring along the road about 35 miles an hour with what looked
like 32 adams appeared imminent a tremendous
Incredible Machine it was a little man Bridgeway dearborn
Cup with that we really say I was getting it it was a group alone I was struck by the
similarity that machine really human word just suppose you’re sitting at the
controls researchers asked sources of energy are you gonna sit back and forth your
arms a murder run itself into a ditch are you going to keep both hands firmly
on the wheel in control and directors produce Pacific workwear papers ship to you you’re in the driver’s seat is either
very law that gives a success is a two-edged sword we must control were thinking the same
rule I can remember you ally for success welfare because nobody
ever dreamed over it was over his family that very same working really well
together is ordinary uses it for good of a baby this is the strangest
secret in the world why do I see a stranger where do I go to the secret actually it
is a secret at all it was first promoted aggressively
earliest wiseman it appears again and again throughout the Bible but very few
people have learned it understand it its latest reviews drivers are equally
strange reason it virtually remains a secret I believe that you could go out and
walked down the main street of your account to this one minute after another
with the secret to success is you probably wouldn’t want to do when
minimum monthly could this information is she normally
valuable to us if we really understand it and abroad Israeli border is not only for our own
lives with the lives of those around us our families employees associates the secret
improves right should be exceeding adventure it
should never be a bore the man should be fully be around I’m he
should be glad to get outta bed in the morning he should be doing a job he likes to do
because he does it will one time I heard growth parish in the
great late editor in chief for The to reveal daily bread maker speech really concluded his speech he said
something I’ve never gotten he said my years in the newspaper
business income this year several things among them the people basically good and that we came from some players then
we’re going someplace so we should make our time here an
exciting adventure the architect of the universe didn’t
build a stairway leading nowhere the greatest teacher or the Carpenters from the plains and
generally gave us a secret or even came again Beijing believe so shall it be done and EU have explained the strangest secret in
the world how it works known this I don’t want to explain how
you can prove yourself the enormous richard is possible in your own life that putting the secret to a practical
test I want you to make it appears to be a rest 30 days it isn’t going to be easy but if
you give it a good try it will completely change your life for
the better the regular seventeenth-century sure Isaac Newton the English
mathematician and natural philosopher gave us the Metro laws of physics which
abrasion which the human beings have a duty to move into bodies in the univers in one these large is that for every
action there is an equal and opposite reaction
serb restated as it approached you and me it means we can achieve nothing without paying the price the results of
your 30-day experiment will be in direct proportion to the effort you put forth to be a doctor you estate appraisal on
years a difficult study to be successful in selling to remember
the teacher succeed is to the extent of his ability to sell showing her family’s own ideas selling
education in schools showing our children. on the advantages
of living the good honest life showing our associates and employees on
the important to being exceptional people to work or speak
professional show yourself but to be successful in selling our way to the
good life we must be willing could pay the price so what is that
price where which many things first understanding emotionally as well
as intellectually that we were literally become what we
think about it that we must control north of the border control our lives its understanding fully that a she’s so
so shall you reap second is carried away or feathers from
the murdered intermediate this story it was divinely
designed to do is the realization that your limitations
are self-imposed and the opportunities for you today are
enormous beyond belief is rising above narrow minded pettiness
and Prejudice and third is using all your courage to
force yourself to think positively on your own problem to set a definite and clearly defined
goals for yourself director marvelous mine think about your goal from all
possible angles to let your imagination speculate freely
upon many different possible solutions to refuse to believe there are any
circumstances sufficiently strong to defeat you in the accomplishment of your
papers to act promptly and decisively when your
course is clear gonna keep constantly aware of the fact
that you are at this moment standing in the middle with your own
acres have died when his rhetoric and will use the pointer and forth save at least 10 percent every dollar you burn is also
remembering that no matter what your present job it is enormous possibilities if you’re willing
to pay the price ministers will be important points in a
price each was misplayed to achieve the wonderful life you can be ours it is a
course worth any price one you will become what do you think
about to remember the word imagination image
in my head begin to store 3 courage concentrate on your goal
everyday for save 10 percent of what you earn
inferred action ideas are worthless in this week German alternate outline the 30-day test
I want you to make you keep in mind that you have nothing to lose by making
mister mister everything you could possibly want to
gain there are two things that may be said everyone each was one something each risk is
afraid to something I want you to write on the card what it
is you want more than anything else it may be more
money pressured by 2w in camera maker specific
amount of money it may be a beautiful home it may be
success at your job it may be a particular position like it
could be a more harmonious family features want something the right down
on your card specifically what it is you want make sure it’s a single goal and clearly
defined you need to show it to anyone the secret but carry it with you so that you can
look at it several times a day think about a demerit cheerful relaxed
possibly way each morning when you get up immediately years from the work force
from to get outta bed for something to live for look at every chance you get during the
day and just before going to bed at night treasurer Kevin remember that you must
become what you think about him since you’re thinking about your goal you
realize too soon it will be yours in fact issuers really them on which you
write it down can begin to think about it look at the
abundance of around you as you go about your daily
business you have as much right to this abundance as any other living creatures is yours for the asking now we come to
the difficult part difficult because it is the formation abroad is probably
bring you have it then you have written it is reformed
$1.4 mil over it will follow you for the rest of your
life stop thinking about what it is you fear addition to fear for their negative
thought the gym your consciousness replace it with a mental picture of your
parents even with logo kirkum times when you feel like giving
up is easier for you would do anything negative even positive results were only
five percent researchers were you must begin now to place yourself in
that group for thirty days you must take control of your mind it will think about only what you
permitted to be good each day because they did a test do more than you have to do in addition
to maintaining a cheerful positive outlook give yourself more than you’ve ever done
before do this knowing that your returns in my eyes must be in direct proportion
to what you do the moment you to set a goal to work
toward you’re immediately a successful person
your than a minute career success in category of people who
know where they’re going at every 100 people you belong to the
top five don’t concern yourself too much with how
you’re going to achieve your goal leave it could take me to a power greater than
yourself all you have to do is no where you’re
going the answers will come to you but their
own accord and at the right time remember these words from the Sermon on
the Mount remember tomorrow keep them constantly before you this
month on your test and ask and it shall be given you sheik initial find not initially opened into you for everyone met sq receive it either secret funded the mid-market it shall be opened is marvelous in a
simple as that the secret in fact it’s a simple dinner seemingly
complicated weird it’s difficult for an adult to understand it all we need is a purpose and faith for 30 days do your very best if your salesman going to be you’ve
never done before not even a hectic fashion but with a condom cheerful assurance that
time well spent will give you the abundance in return you deserve reward your home maker double 232 is to
completely giving up yourself without thinking about receiving anything in
return you’ll be amazed at the difference it
makes the right no matter what your job do is you’ve never done it before for 30
days if you kept your goal before you every
day you wonder in moreover this you like youporn Dorothea Brande the outstanding editor
and writer discredit yourself and tell us about your fine book wake up and live the entire philosophy
is reduced to the words act as though it were impossible to fail
you she made a road test with tertiary a
very different airline pushes you want to go there were only six years no you make your test for 34 days doster jitters to give you made up your
mind to stick with it you see by being persistent you’re
demonstrating faith for systems is simply another word for
free if you didn’t have reviewed never pressures if you should clear your first 30 days
by that I mean suddenly find yourself overwhelmed by negative charge you gotta start over
again from that point then go 30 more days gradually you have it will form injury
five years or whatever wonderful minority do virtually nothing
is impossible and don’t forget the card it’s vitally
important as you begin this new way of living 11 said it occurred write your goal
whatever it may be on the other side write the word
reported from a certain amount ask and it should be given you sheik the secret initial find not it should be opened into you nothing great was ever
accomplished without inspiration she did during these crucial
first 30 days your own inspiration is kept to a peak and above all don’t worry worry brings
fear and fear scripted the only thing we can cause you to worry
do you to refuse to do it all yourself know that all you have to do is hold
your goal before you everything else will take a richer
remember also to keep calm and cheerful still get paid the things you know are
you in get you of course this decision is this is difficult
emotionally why should I bother where look at the alternative no one
wants to be afraid you no one really wants to be a mediocre individual no one
wants American history fair with your YouTube feared restoration therefore remember that you wish to reap
that which you so if you’re so negative thereof your life
will be filled with negative things if you show prices are your local
butcher for successful in positive gradually rather tendency to forget
where the word on this recording paid often keep reminding yourself what
you must do to go on this you have it gather your family around at regular
intervals are missing it was considered you know most men will tell you that
they want to make money without understanding the law the only people who make money working
amid the rest is most earn money this is what causes those who
keep looking for something to do with your free ride to Fremont the only way to earn money is by
providing people with services or products which are needed
and useful we exchange our time in our product is shipped distributed
newsworthy therefore the lawyers that are permitted
to return will be in direct proportion to our service success is not to resort to making money
making money is the result is success their successes
in direct proportion worshipers most people have a small
backwards they believe it your success or your dad
money the truth is that you can only earn
money after your situation is like this jury matters have
reproduced or redistributed give me he’d and generate the wood how many men and women do you know where
usable here today to take the same attitude toward life there are millions we’ve got to put the
few even before we can expect pete likewise we’ve
got to be a serious first before we can expect many don’t concern
yourself with the money be of service build work dream create do there’s a new phone is no
limit to the prosperity and abundance will come to you fresh 30-year was going to go to your
mutual exchange every person who contributes to the secret
Prestbury West Ashley incurred in some from danger Turnbull not come to closure
but it must come to you from someplace because restaurant for every action there is an equal and opposite reaction as you go daily to your 30-day disputed
remember that your success will always be measured data quality and quantity should this you render and money is a
yardstick for measuring the service no man can get
rich yourself and messy and Richard others here no
exceptions to the mall even drive down any street america in
from your car estimate the services being rendered whether people living on
the street did you ever go to be sure to check
before it’s interesting sir Mike ministers and priests through
other devoted people measure the richer in a room with a spiritual it again be returned to equally share
this: which is yours truly understood any
thinking person can get his own fortune he wants more he was being more serious
traditionally received his return he was yours years only to reduce your
service this is the price you must pay for what you want if you
believe you can enrich yourself by diluting others you can and only by
deluding yourself it may take some time but just as surely
as you breathe you’ll get back what you put out don’t ever make a mistake in thinking
you can reproduce it’s impossible the prisons in the streets with the only
water filled with people who tried to make new laws just for the videos we may avoid the resume broo but you’re
a greater loss but cannot be broken an outstanding medical doctors reported
at six steps will help you realize success one set yourself a definite go to good running yourself down 3 stop
thinking about all the reasons why you cannot be successful and instead they do
all the reasons where you can for treasure attitudes back to your
children and to discover we first got the idea
you could be successful effectuate a veggie 5 change the image
you have yourself by writing out a description of the person you would like
to be m6 at the park the successful person you
have decided to be said the doctor who wrote those words is a
noted West Rocha Turkish yesterday with the Herald think do with
the experts since the dawn of recorded history told you you must do pay the price by
becoming the person you want to come isn’t nearly as difficult as reviewing
successfully make your 30-day testing repeated and repeated again an Eastern it will become more reported
you do you want your YouTube every move to the other way you have this new way in the floodgates
have opened in June open pore over you more which is really a dream to just
read money year’s roster but there was more
important you have peace you be in that wonderful
minority who did come cheer for successful writers scared to be you have nothing to lose
did you ever hear life to win this year or next year and thank you

Law & Order: SVU – Two Young Lives Torn Apart (Episode Highlight)

– You lied to the police and to your friends. Is that your story? – Yes.
I’m not proud of it. – You did so because
your friends were taunting you that you hadn’t scored? – I wouldn’t put it
that way. – You’d call it
making love? Or cherry picking? – Objection.
– It’s the name of the club. – Overruled. – Doesn’t matter
what I’d call it. I didn’t do anything
Abby didn’t want. – So she went to the police,
testified on the stand, was publicly humiliated
and ostracized by her friends for something
that she made up? – No, she probably thinks
she was raped. – Well, what does
that tell you? – That she thinks that now,
but she did want it at the tim. – How can you be sure
of what she was thinking or what she wanted? – Objection.
Badgering. – Witness will answer. – I don’t know
if I can be sure, but she didn’t say no. – She didn’t say it
or you didn’t hear it? – I don’t know.
– Did you ever ask her? – No.
– Did you ever hear a yes? No, because you weren’t
listening to her at all, were you? Your only concern was
getting what you wanted, scoring, making it up
onto that wall. Well, congratulations,
you made it. Nothing further. [tense music] ♪ ♪ – Hey.
– Hey. – I just wanted
to thank you. That was a good cross. You know, no matter
what the jury decides, you did your job. – Did I? It was always
a murky case. – Exactly the kind
that we need to be fighting. The world is changing. We need new rules. – Rules of sexual engagement
for teenagers? – Yes. California just passed
affirmative consent. – We’ll see how that goes. – Well, something
needs to change. The problem is
is that teenage boys even in college
don’t know what behavior might constitute rape. We need to make
the lines clearer. [knock at door] – Jury’s in. – Here we go. – Members of the jury,
have you reached your verdict? – We have, Your Honor. – On the felony count
of attempted rape, how do you find? – We find the defendant,
Chris Roberts, not guilty. – On the misdemeanor count
of forcible touching, how do you find? – Not guilty, Your Honor. – On the misdemeanor count
of sexual misconduct in the first degree,
how do you find? – Guilty. [crowd murmurs]
– What? – Members of the jury, the court thanks you
for your service. You are free to go. [bangs gavel] – I hope you’re happy. Look what you did
to my son. – Abby.
– Chris. – Don’t you talk to her.
Don’t you even look at her! – I’m sorry. – Now you’re sorry? – Don’t you apologize
to him, sweetie. – Now is not the time. – Abby, you have nothing
to apologize for. – You can’t tell me
that she didn’t know what was gonna happen
when she went into that room. – You all can lie to yourselves
all you want! We know exactly
what your son is! And now he’s on the registry,
and everyone will know! – We know what your daughter i!
– Enough! Enough! Enough! Enough! [gentle music] ♪ ♪ – Chris. – Abby, let’s go. ♪ ♪

My Car. My Boyfriend. My Responsibility.

(upbeat music) Carmen Rolone. Morning Carmen. Morning. You are charged with going through a red light on Dean Street. You’re also charged with going through a red light on Roger Williams Avenue and Elmwood Avenue. And you have a parking ticket. I’m taking these one at a time. At Roger Williams and Elmwood Avenue, you’re charged with going through a red light. Do you recall that? I see here, that it, brakes. You saw there, what? The light brake. Oh, so you stopped? Yes. Okay, well, let’s take a look. This is number 724. Oh, at least I got to sign. I thought I put the light on. There’s a sign on the corner that says, right on red, after stop. Okay, did you stop? It doesn’t look like. No? No. (crowd laughing) Sorry. But we know your eye sight is good, that’s good. And you have a second one on Dean Street and Route 10. Yeah, I don’t know about that one. Did you stop at that light? I don’t know about that one. Probably my boyfriend. Your boyfriend was driving the car? Yes. Did you question him about this? Yes. And what did he say? He says a construction. He said what? Construction. In the Route 10. And it’s a lot of bad driver. There were bad drivers? No me. No your boyfriend? No, he’s a good driver. He’s a good driver. So he didn’t go through the light? I don’t know. Oh you don’t know. I don’t get that ticket, They send it today. It’s under your name. Yeah. It’s your car. Yes. Means you’re responsible. Exactly, that’s why I’m here. Did he give you the money? Yes sir, he gave me the money. He gave you the money? Yes. Oh good. Then he’s guilty. Yes, I guess. Alright, we’re gonna take a look at it, just relax. This is on Dean Street in Route 10. The light is red. Wow. No. You make the decision, is he guilty? Yes he is. He’s very guilty. Okay. It’s gonna cost you 115 dollars. 85 dollars for your boyfriend, and he gave you the money. Yeah. 30 Dollars for a parking ticket on Pearl Street. Pearl Street. And I’m gonna give you a break on the Elmwood Avenue dear right. When you see the sign that says right on red after stop, stop. Okay. Okay. You got that? Yeah I got it. Okay, good luck to you. Thank you. Have a good one. Come on, how cool was that? If you’d like to see more cases like this one, tune into Caught in Providence every week day. Excuse me? You didn’t know Caught in Providence is also a TV show? Oh wow. Your life just got substantially better. To find out what channel we’re on, go to Click on your local listings. Scroll down till you find your hometown. Then start doing your happy dance. That’s it. Move it. Move it. Nice. [Narrator] All rise and hit subscribe, so you don’t miss the latest viral moments like this one. Share these videos and weigh in on the cases. You be the judge. Subscribe now.

Neil deGrasse Tyson Teaches Scientific Thinking and Communication | Official Trailer | MasterClass

One of the great
challenges in this world is knowing enough
about a subject to think you’re right but
not enough about the subject to know you’re wrong. There’s like a gazillion
hours of me on the internet. In almost every case, I’m
talking about the universe– black holes, the big
bang, time travel, God. What I’m going to do
in this MasterClass is teach you how to think. The goal here is
to train your mind how to see the world
differently, how to question what others say. I’ve come to realize that there
are three categories of truth– personal truth,
political truths, and the objective truths
that shape our understanding of the universe. The interesting thing
about an objective truth is that it’s true
no matter what. Imagine that. By the time we’re
done, you will be equipped with some of
the methods and tools so you can turn data into
information, information into knowledge,
knowledge into wisdom. We all have
susceptibility to bias. Search engines on the internet
are the epitome of confirmation bias, and you’re going
to use that as evidence that you are correct? No. The good thing about science is
that it’s true whether or not you believe in it. What does it mean
to be skeptical? What does it mean to
be convinced by data? A proper skeptic questions
what they’re unsure of but recognizes
when valid evidence is presented to change their mind. I will equip you to not
only find objective truths but then communicate to
others how to get there. It’s not good
enough to be right. You also have to be effective. The less connected you are
to what is objectively true, the less likely you will
be able to make decisions that will benefit your life– your life, the life of your
family, and even civilization itself. I’m Neil deGrasse Tyson,
and this is my MasterClass.


The year is wrapping up and a lot of people
are talking about goal setting and what you want to achieve in 2020. But before we even get there, I wanted to
touch on something that you found really interesting and I was kind of surprised by. I had never talked about the law of attraction
or manifestation publicly really, but I did a video on it recently and I talked about
how I manifested $1 million and meeting Oprah and Tony Robbins and Marine Forleo and all
these crazy things that have happened, because I use the law of attraction and I’m a big
believer in the law of attraction. And I know that you might be thinking it’s
a little woo woo, it’s a little hippy dippy, but I believe it to be true because it works. And so I wanted to make a followup video because
the amount of DMs and questions and comments I got from that video has been so overwhelming. And a lot of you are asking me, “Where do
I even start with the law of attraction? Or I’m really interested in it. How do I start manifesting what I really want?” And here’s what I wanted to talk about first. The law is already working for you. So the law of attraction works, even if you’re
not trying to work it. And you might be thinking, “Well, I don’t
have my dream job or my dream car yet, so it’s not working.” And that’s not what I mean. It actually means that good or bad, the law
of attraction is constantly working for you. So whatever energy and vibration you’re putting
out there, is what you’re going to be attracting, good or bad. So the first thing to understand about the
law of attraction is that it’s always working. So if you’re excited to dive deeper into this
topic with me today and how the law of attraction really works and how to manifest anything
you really want, give this video a like hit the subscribe button. Do it already, really it’s quite rude if you’re
here and haven’t subscribed. Make sure you subscribe and hit the bell to
get notified every single time I post a new video. So, first thing is the law of attraction is
always at work, good or bad. It’s more so up to you and what you’re putting
out into the world, that’s what you’re going to attract. If you’re putting out negativity and bad vibes,
then you’re going to get that right back. It’s like a boomerang effect. And what’s really interesting is there was
actually a study done in 2017 that said you are 42% more likely to achieve your goals
and the people in this study were 42% more likely to achieve their goals when they wrote
the goals down over and over again. And they did it on a regular basis. So that’s a big thing that I wanted to talk
about in this video is that, the law of attraction isn’t just about thinking about what you want. It’s also about taking action. And a small action that you can take on a
daily basis is to write down what you want. And that’s a simple thing that’s going to,
based on this study done a couple of years ago by a psychologist in California, make
it 42% more likely that you’re going to achieve it. And the other thing that you need to understand
is that the subconscious mind doesn’t know the difference between reality and what you
want to manifest and attract. So often times when I’m writing down what
I want to attract in my life, I will include things that have and haven’t happened yet. So I’ll say things like, “I’m so grateful
for my health and I’m also so grateful for the home that we’ve got right on the water
in Vancouver.” We don’t have that home yet, but I know it’s
going to happen. So I write it down as if it’s already true,
because that’s another big part of it. So you have to think it, act on it, and believe
that it’s already true and already done in order for something to actually manifest into
reality. That’s really how the law of attraction is
going to fast track and really start working for you in your life. So you have to think it, believe it, see it,
act it, do it as if it’s already true and as if it’s already done. So maybe you’re in a really crappy place in
your life right now, but you need to act on a vibration that is higher, more positive,
and change your outlook and perspective in order to actually achieve great things and
attract good things into your life, because if you’re on a low vibration, the universe,
whatever you want to call it, feels that and what it’s going to serve back to you is crap. And you’re going to get in fights with people
more often, you’re going to attract crappy opportunities, you’re going to create more
friction with people in your life. Whereas when you are in flow and the law of
attraction is really working for you, you’re going to feel like things start to come to
you really easily. And the only way to be in that space is to
be open and to be in a really good, healthy, positive mind frame. So let’s talk about more how you can manifest
that and start acting on that in your own life to start making sure the law of attraction
works for you. So the really simple way to understand this
is that everything in the world has a vibration. Human, nonhuman, doesn’t matter. Everything has a vibration. And you’ll notice that when you’re having
a really good day or when you’re in a really good mood, things just seem a little bit easier. And that’s a perfect example of the law of
attraction at work. So if you’re having a bad day and one thing
goes wrong, does it oftentimes feel like everything’s going wrong? That means that you’re in a negative vibration
or a low vibration and you’re only attracting other low frequencies, people, opportunities,
conversations, etc. So good mood, good head space equals good
opportunity and attracting the right things and being more in flow in your life. That’s just a really simple thing to understand. So getting yourself in a positive head space
right off the bat is so important. That’s where having a gratitude journal in
the morning is vital because if you’re grateful, as soon as you wake up, you put yourself into
a good receiving head space to receive the things that you really want. You’re basically a magnet for whatever it
is that you’re putting out there. So simply put, the law of attraction is basically
a magnet for whatever it is that you’re focusing on. So if you’re focusing on bad things, you’re
going to get more bad things. If you’re focusing on good things, you’re
going to get more good things. So the key to making the law of attraction
work for you is really twofold. The first thing is, you have to know what
you want. If you’re feeling kind of lost and you’re
like, “I don’t even know what I want manifested in my life,” start with something small. Start with things like, “I am healthy, I am
fit. I am working out once a week.” If you’re not doing that right now, write
it down, put it in your schedule, and that is the law of attraction because you’re saying
the things that you really want to feel and you’re taking the action to do them. So start with small things. You don’t have to start with these big audacious
goals, but you have to get clear on what you want. If the universe is unclear on what you want
or what you want to attract, you’re not going to get it because you’re sending mixed messages. And you also have to understand that the universe
doesn’t hear negative. So if you say something like, “I don’t want
to be late,” you’re going to be late because it only hears “I want to be late.” It doesn’t hear, “I don’t want to be late.” So really be conscious of your thoughts and
the things that you’re putting out there. If you’re constantly saying, “I’m broke,”
guess what? That’s what the universe is going to hear
and it’s going to serve it back to you. So you have to put yourself in a head space
of what you want and what you want to be achieving in your life and putting it out there constantly
in order for the university to serve it back to you. So getting clear on what you want and by just
writing some things down, that’s a great way to gain that clarity. And just checking in with yourself is a great
way to get in some clarity. Also, anywhere in your life where you feel
a little bit of jealousy or envy, that’s a pretty good clue that that thing is probably
something that you really want, but you’re scared to say out loud. So start writing it down. Start playing around with those ideas and
thoughts because those could be the things that you really are after in this life, but
you’re just afraid to go after them. And the second part of this is, once you know
what you want, you need to believe that it is already true and act on it as already true. I gave an example in my last video that before
I even had a car, I would go to really nice dealerships and I would test drive cars just
to know what it felt like because I was like, “I want to act and believe that this is already
true and happening for me.” And then I got the car that I really, really
wanted a couple of years later. So it doesn’t always work overnight. Manifestation doesn’t always happen overnight,
but it really is simple when you break it down. Thoughts become things and the more that you
think about good things and you’re in a good head space, the more great things you’re going
to attract into your life. And it’s simply is just being more conscious
of how you’re showing up, when you wake up, when you get up out of bed in the morning,
and you can probably see the law of attraction at work, most prevalent in your relationships. If you’re getting up in the morning and you’re
not even saying hello to your partner or your boyfriend, or you’re in a really crappy mood
the moment you get out of bed, your partner is probably not in the best mood either and
probably doesn’t even really want to be around you. So that right there is the law of attraction
at work. What you’re putting out, you’re getting back. So being really conscious of your state and
how you’re showing up in the world is the first place to start with the law of attraction. But the really simple way to understand this
is, the thoughts that you think become the things that become reality in your real life. And in order to manifest what you really,
really want, you have to believe it, you have to see it, you have to act on it, and you
have to think about it and write it down. You’re 42% more likely to achieve what you
want when you write it down. So the best place to start is, one of the
biggest questions I got asked is, where do I even start with this? The best place to start understanding the
law of attraction and where I really into it was I actually read the book The Secret,
which is probably one of the most popular books on the topic. So I can link to that below in the description. And then there’s also a movie called The Secret,
so you can watch that too. You’ll be astonished when you watch it, the
power of your thoughts and how you are creating your own reality right now with your thoughts. And that’s why it’s so important to be so
conscious and aware of the things that you’re thinking. So that’s my little breakdown of what it really
means and how you manifest whatever you want because it is possible. If you watch this video, it’s crazy the things
that I manifested in my life and it all starts up here. And you can look at it in your daily life
and especially as an entrepreneur, if you are an entrepreneur, all of the things that
you create in your business didn’t exist before you thought about it. Disney didn’t exist before Walt Disney thought
about it in his brain. If he didn’t think about it first and act
on it, it wouldn’t have happened. That’s the law of attraction. You can manifest anything you want, but you
have to put yourself in the right head space. So that’s my little breakdown. Let me know what your big takeaway was from
this. What do you want to manifest in your life? Let me know in the comments below. If you enjoyed this, hit that like button. Be sure to subscribe and hit the bell to get
notified every single time I post a new video. Thank you so much for watching and make sure
you check out this video on how I manifested $1 million. It’s pretty crazy. See you in the next video. Bye.

Caller: What’s Wrong with Dem Debates Being Skewed Right?

Let’s go next to, uh, let’s go to Mike from
Georgia at the seven Oh six area code. Mike from Georgia. What’s going on? [inaudible] Hey David, how are you doing? Good, thanks. Okay. So, uh, I had a question. So, um, we hear a lot about, um, you know,
in the debate that they asked, uh, right-wing framed questions. But don’t we need a right-wing frame questions
if we’re going to be taking on, you know, the uh, the Republican establishment or really
just the establishment as a whole. Yeah. So, so you’re asking a very important question. So here’s the thing, some during, during democratic
debates, the point is to best figure out who of the democratic candidates, really it’s
for two things. Whose policies do you most agree with? And we are also making judgments about electability. We are imagining the candidates on the stage
debating Donald Trump. So it seems like what you’re pointing out
is at a certain point, the democratic nominee is going to have to face Trump and is going
to have to face Republican arguments. Therefore, isn’t it logical for the moderators
to be making some of those Republican arguments in questioning the Democrats? Is that sort of what you’re saying? Yeah, yeah. That’s basically what I’m saying. Here’s the problem with it. When the moderator is framing up a question
for all of the people on the stage that’s not about asking a particular candidate how
something about their policy will work. When you frame the entire question in a way
that is a Republican slant, you’re in a sense discrediting the fact that this is even being
discussed in particular terms and that’s why it’s so problematic. If you have different Democrats up on the
stage and someone wants a public option for health care, someone wants Medicare for all,
some someone wants a phased in Medicare, you know you have all these, all these different
things. You want that to be debated in a way that
is sort of fair and neutral and let the candidates frame their positions and if they want to
bring up what it is that Donald Trump wants to do, fine. When the monitor moderators a priori frame,
the entire question where the logical answer, the right position is one. That is what Republicans are advocating for
or more to the right. Not only is it not the point of the democratic
debates, it also is helping the more conservative candidates up on the stage. And so we just don’t want it. That’s not the role the moderators were supposed
to have. Okay. Yeah. Yeah, that, that definitely makes sense. Um, I always just kind of found a hypocritical
that they’re supposed to come off as a neutral force and yet they seem to go in more towards
a, uh, a Republican direction or really setting up all these trap questions that you can’t
really, you can’t really wiggle your way out of unless you attack the framing of the question. That’s another good point, which is that it
took to properly handle that you’re putting the candidates in a position where they either
have to go after the moderators for the framing, which they should do. And I’m glad when they do it, but that takes
time away from actually figuring out who onstage has the best policy. And so it’s also a distraction in that way. Oh yeah. And, and that’s kinda like my, my problem
with debate other than the fact that I don’t know how much they’ll, they’ll change the
course of the election. Cause I mean, I feel like most people kinda
have an idea of who they want to vote for. Yeah. At this point in the game, this late in the
game, the debates will do very little to change public support other than if someone blunders
terribly and they will then be hurt. But it is very difficult at this point in
the game to really gain very much by doing well in the debates because people are mostly
familiar with the candidates and with their positions. Yeah. All right, well you pretty much answered my
questions, so thank you very much David. All right, thanks Mike. Great to hear from you.

Oscar thanks Lily for her help in the government | FPJ’s Ang Probinsyano (With Eng Subs)

My beloved countrymen, this Holy Week, we are remembering
the sacrifices of our Lord. Most of us understand
it very well, because we also
suffered under the previous
administration. Now that we’ve moved on
from that dark phase, we will continue
to work in unity so that we can restore
peace and order. Many victims of the
previous administration hope of having their
normal lives back. And I’m so grateful
for the people who offered their help especially those from
the business community led by the chairwoman of Magkaagapay sa
Pagbangon Project Lily Ann Cortez. Even back when I was
still hiding with Vendetta, Lily was there to
support my advocacies. Until now, she continues to
support the government. I can totally
relate to them. I also lost my family. So I know how painful it is to lose the people you love. Don’t you have any
relatives left, Lily? I’m sorry for asking. No, it’s fine. I have no family to
share my riches with, so I better share it
to other people. And I’m happy because you’re all there for me. You are my family now. I thank God… …for letting
our paths cross. For letting me meet
Cardo and the Vendetta. Thank you for providing the
president with information. It’s important that he’s
immediately informed about everything concerning
national security. Lily. General Borja, I was
looking for you earlier at the project’s
inauguration. I’m sorry, but I was
really busy. But I did hear about
the generous donation you gave to the NGOs. That’s just the beginning. Is there a problem? It’s nothing. I was just thinking that we
still have many things to do before we attain the
president’s goal of ridding our country
of criminals. I’m with you there. I’m sorry,
but I still have no information
regarding Hipolito. How about you? Have you
found anything? Nothing yet, but if we
continue to work together, I’m sure we’ll eventually
capture him. I might be taking too much of
your time, so I’ll go now.

22. The Boltzmann Constant and First Law of Thermodynamics

So, I had to leave you in the
middle of something pretty exciting, so I’ll come back and
take it from there. So, what is it you have to
remember from last time? You know, what are the main
ideas I covered? One is, we took the notion of
temperature, for which we have an intuitive feeling and turned
it into something more quantitative,
so you can not only say this is hotter than that,
that’s hotter than this, you can say by how much,
by how many degrees. And in the end we agreed to use
the absolute Kelvin scale for temperature.
And the way to find the Kelvin scale, you take the gas,
any gas that you like, like hydrogen or helium,
at low concentration, and put that inside a piston
and cylinder. That will occupy some volume
and there’s a certain pressure by putting weights on top,
and you take the product of P times V,
and the claim is for whatever gas you take,
it’ll be a straight line. Remember now, this is in Kelvin.
Your centigrade scale is somewhere over here,
but I’ve shifted the origin to the Kelvin scale.
So, somewhere here will be the boiling point of water,
somewhere the freezing point of water;
that may be the boiling point of water.
And if you took a different amount of a different gas,
you’ll get some other line. But they will always be
straight lines if the concentration is sufficiently
low. In other words,
it appears that pressure times volume is some constant.
I don’t know what to call it. Say c,
times this temperature. And you can use that to measure
temperature because if you know two points on a straight line
then you know that you can find the slope and then you can
calibrate the thermometer, then for any other value of
P times V that you get, you can come down and read
your temperature. That’s the preferred scale,
and we prefer this scale because it doesn’t seem to
depend on the gas that you use. I can use one;
you can use another one. People in another planet who
have never heard of water–they can use a different gas.
But all gases seem to have the property that pressure times
volume is linearly proportional to this new temperature scale,
measured with this new origin at absolute zero.
There is really nothing to the left of this T=0. The next thing I mentioned was,
people used to think of the theory of heat as a new theory.
You know, we got mechanics and all that stuff–levers and
pulleys and all that. Then, you have this mysterious
thing called heat, which has been around for many
years but people started quantifying it by saying there’s
a fluid called the caloric fluid and hot things have a lot of it,
and cold things have less of it, and when you mix them the
caloric somehow flows from the hot to the cold.
Then we defined specific heat, law of conservation of this
caloric fluid that allows you to do some problems in calorimetry.
You mix so much of this with so much of that,
where will they end up? That kind of problem.
So, that promoted heat to a new and independent entity,
different from all other things we have studied.
But something suggests that it is not completely alien or a new
concept, because there seems to be a conservation of law for
this heat, because the heat lost by the
cold water was the heat gained by the hot water.
I’m sorry. Heat gained by the cold water
was the heat lost by the hot water.
So, you have a conservation law. Secondly, we know another way
to produce heat. Instead of saying put it on the
stove, put it on the stove, in which case,
there is something mysterious flowing from the stove into the
water that heats it up, I told you there’s a different
thing you can do. Take two automobiles;
slam them. This is not the most economical
way to make your dinner but I’m just telling you as a matter of
principle. Buy two Ferraris,
slam them into each other and take this pot and put it on top
and it’ll heat up because Ferraris will heat up.
The question is what happened to the kinetic energy of the two
cars? That is really gone.
So, in the old days, we would say,
well, we don’t apply the Law of Conservation of Energy because
this was an inelastic relationship.
That was our legal way out of the whole issue.
But you realize now this caloric fluid can be produced
from nowhere, because there was no caloric
fluid before, but slamming the two cars
produce this extra heat. So, that indicates that perhaps
there’s a relation between mechanical energy and heat
energy–that when mechanical energy disappears,
heat energy appears. So, how do you do the
conversion ratio? You know, how many calories can
you get if you sacrifice one joule of mechanical energy?
So, Joule did the experiment. Not with cars.
I mean, he didn’t have cars at that time, so if he did he
would’ve probably done it with cars.
He had this gadget with him, which is a little shaft with
some paddles and a pulley on the top, and you let the weight go
down. And I told you guys the weight
goes from here to here, the mgh loss will not be
the gain in ½ mv^(2). Something will be missing.
Keep track of the missing amount.
So many joules–but meanwhile you find this water has become
hot. You find then how many calories
should have gone in, because we know the specific of
water, we know the rise in
temperature, we know how many calories were produced.
And then, you compare the two and you find that 4.2 joules=1
calorie. So, that is the conversion
ratio of calories to joules. One joule, 4.2 joules of
mechanical energy. So, in the example of the
colliding cars, take the ½ mv^(2) for
each car, turn it into joules, slam them together.
If they come to rest, you’ve lost all of that,
and then you take that and you write it as–divided by 4.2 and
that’s how much calories you have produced.
If the car was made of just one material, it had a specific
heat, then it would go up by a certain temperature you can
actually predict. Okay.
So today, I want to go a little deeper into the question of
where is the energy actually stored in the car,
and what is heat. We still don’t know in detail
what heat is. We just said car heats up and
the loss of joules divided by 4.2 is the gain in calories.
Now, we can answer in detail exactly what is heat.
That’s what we’re going to talk about today.
When we say something is hotter, what do we mean on a
microscopic level? In the old days when people
didn’t know what anything was made of, they didn’t have this
understanding. And the understanding that I’m
going to give you today is based on a simple fact that everything
is made up of atoms. That was not known,
and that’s one of the greatest discoveries that,
in the end, everything is made up of atoms,
and atoms combine to form molecules and so on.
So, how does that come into play?
For that, I want you to take the simple example where the
temperature enters. That is in the relation
PV equal to some constant times temperature.
Do you know what I’m talking about?
Take some gas, make sure it’s sufficiently
dilute, put it into this piston, measure the weights on top of
it, divide it by the area,
to get the pressure, that’s the pressure,
that’s the volume. The volume is the region here,
multiply the product; then, if you heat up the gas by
putting it on some hot plate, you’ll find the product
PV increases, and as the temperature
increases, PV is proportional to T.
We want to ask what is this proportionality constant.
Suppose you were doing this. In the old days,
this is what people did. What did we think should be on
the right-hand side? What is going to control this
particular constant for the given experiment?
Do you know what it might be proportional to?
Yes? Student: Amount of gas?
Professor Ramamurti Shankar: Amount of gas.
That’s true, because if the amount of gas is
zero, we think there’s no pressure.
When you say “amount of gas,” that’s a very safe sentence
because amount measured by what means?
By what metric? Student: Probably number
of particles? Professor Ramamurti
Shankar: Right. Suppose you were not aware of
particles. Then, what would you mean by
“amount of gas?” Student: Mass.
Professor Ramamurti Shankar: The mass.
Now, if you guys ever said moles, I was going to shoot you
down. You’re not supposed to know
those things. We are trying to deduce that.
So, put yourself back in whatever stone ages we were in.
We don’t know anything else. Mass would be a reasonable
argument, right? What’s the argument?
We know that if you have some amount of gas producing the
pressure, and you put twice as much stuff,
you would think it will produce twice as much pressure.
Same reason why you think the expansion of a rod is
proportionally change in temperature times the starting
length. So, this mass is what’s doing
it. So, it’s proportional to mass.
It’s a very reasonable guess. So, if you put more gas into
your piston you think it’ll produce more pressure.
That’s actually correct. So, let’s go to that one
particular sample in your laboratory that you did.
So, put the mass that you had there.
Then, you should put a constant still.
I don’t know what you want me to call this constant,
say, c prime. This constant contains
everything, but I pulled out the mass and the remaining constant
I want to call c prime. This is actually correct.
You can take a certain gas and you can find out what c
prime is. But here is what people found.
If you do it that way, the constant c prime
depends on the gas you are considering.
If you consider hydrogen gas, let’s call that c prime
for hydrogen. Somebody else puts in helium
gas. Then you find the c
prime for helium is one-fourth c prime for hydrogen. If you do carbon,
it’s another number. c prime for carbon is
c prime for hydrogen divided by 12.
So, each gas has a different constant.
So, we conclude that yes, it’s the mass that decides it
but the mass has to be divided by different numbers for
different gases to find the real effective mass in terms of
pressure. In other words,
one gram of hydrogen and one gram of helium do not have the
same pressure. In fact, one gram of helium has
to be divided by 4 to find its effect on pressure.
So, you have to think about why is it that the mass directly is
not involved. Mass has to be divided by a
number, and the number is a nice, round number.
4 for this and 12 for that, and of course people figure out
there’s a long story I cannot go into, but I think you all know
the answer. But now we are allowed to fast
forward to the correct answer, because I really don’t have the
time to see how they worked it out,
but from these integers and the way the gases reacted and formed
complicated molecules, they figured out what’s really
going on is that you’re dividing by a number that’s proportional
with the mass of the underlying fundamental entity,
which would be an atom. In some case a molecule,
but I’m just going to call everything as atom.
So, if things, like, carbon,
as atoms, weigh 12 times as much as things called hydrogen,
then if you took some amount of carbon, you divide it by a
number, like, 12 to count the number of
carbon atoms. Okay, so hydrogen you want to
count the number of hydrogen atoms.
So then, what really you want here is not the mass,
but the number of atoms of a given kind.
We are certainly free to write either a mass or the number of
atoms, because the two are proportional.
But the beauty of writing it this way, you write it in this
fashion, by this new constant k, k is
independent of the gas. So, you want to write it in a
manner in which it doesn’t depend on the gas.
You can write it in terms of mass.
If you did, for each mass you’ve got to divide by a
certain number. TThen once you divide it by the
number you can put a single constant in front.
Or if you want a universal constant, what you should really
be counting is the number of atoms or molecules. So, you couldn’t have written
it that way until you knew about atoms and molecules and people
who are led to atoms and molecules by looking at the way
gases interact, and it’s a beautiful piece of
chemistry to figure out really that there are entities which
come in discreet units. Not at all obvious in the old
days, that mass comes in discreet units called atoms,
but that’s what they deduced. So, this is called the
Boltzmann Constant. The Boltzmann Constant has a
value of 1.4 times 10^(-23), let’s see, joules/Kelvin. That’s it.
Or joules/Kelvin or degrees centigrade. So, this is a universal
constant. So, now what people like to do
is they don’t like to write the number [N], because if you write
the number, in a typical situation,
what’s the number going to be? Take some random group gas.
One gram, two grams, one kilogram,
it doesn’t matter. The number you will put in
there is some number like 10^(23) or 10^(25).
That’s a huge number. So, whenever a huge number is
involved, what you try to do is to measure the huge number as a
simple multiple off another huge number,
which will be our units for measuring large numbers.
For example, when you want to buy eggs,
you measure in dozens. When you want to buy paper,
you might want to measure it in thousands or five hundreds or
whatever unit they sell them in. It’s a natural unit.
When you want to find intergalactic distances,
you may use a light year. You use units so that in that
unit, the quantity of interest to us is some number that you
can count in your hands. When you count people’s height,
you use feet because it’s something between 1 and 8,
let’s say. You don’t want to use angstroms
and you don’t want to use millimeters.
Likewise, when you want to simply count numbers,
it turns out there’s a very natural number called Avogadro’s
Number, and Avogadro’s Number is 6
times 10^(23). There’s no unit.
It’s simply a number, and that’s called a mole.
So, a mole is like a dozen. We wanted to buy 6 times
10^(23) eggs, you will say get me one mole of
eggs. A mole is just a number.
It’s a huge number. You can ask yourself what’s so
great about this number? Why would someone think of this
particular number? Why not some other number?
Why not 10^(24)? Do you know what’s special
about this number? Yes?
Student: [inaudible] Professor Ramamurti
Shankar: Yes. If you like,
a mole is such that one mole of hydrogen weighs one gram.
And hydrogen is the simplest element with a nucleus of just a
proton and the electron’s mass is negligible.
So, this, if you like, is the reciprocal of the mass
of hydrogen. In other words,
one over Avogadro’s Number is the mass of hydrogen in grams,
of a hydrogen atom in grams. So, you basically say,
I want to count this large number so let me take one gram,
which is my normal unit if you’re thinking in grams.
Then I ask, “How many hydrogen atoms does one gram of hydrogen
contain?” That’s the number.
That’s the mole. So, if you decide to measure
the number of atoms you have in a given problem,
in terms of this number, you write it as some other
small number called moles, times the number in a mole,
and you are free to write it this way.
If you write it this way, then you write this nRT,
R is the universal gas constant.
What’s n times the Boltzmann Constant.
N_0 times the Boltzmann Constant.
That happens to be 8.3 joules per degree centigrade or per
Kelvin. Right?
The units for R will be PV, which is units of
energy divided by T. In terms of calories,
I’d remember this as a nice, round number.
Two calories per degree centigrade.
Degrees centigrade and Kelvin are the same.
The origins are shifted, but when you go up by one
degree in centigrade or Kelvin, you go the same amount in
temperature. So, this [R]
is what they found out first, because they didn’t know
anything about atoms and so on. But later on when you go look
under the hood of what the gas is made of, if you write it in
terms of the number of actual atoms,
you should use the little k, or you can write it in
terms of number of moles, in which case use big R. And the relation between the
two is simply this. If you’re thinking of a gas and
how many moles of gas do I have? For example,
one gram of hydrogen would be one mole.
Then you will use R. If you’ve gone right down to
fundamentals and say, “How many atoms do I have?”
and you put that here, you will multiply it by this
very tiny number. Alright.
Now, you start with this law and you ask the following
question. On the left-hand side is the
quantity P times V.
On the right-hand side I have nRT, but let me write it
now as NkT. You guys should be able to go
back and forth between writing in terms of number of moles or
the number of atoms. You’ll like this because all
numbers here will be small, of the order 1.
R is a number like 8, in some units,
and n would be 1 or 2 moles.
Here, this N will be a huge number, like 10^(23).
k will be a tiny number like 10^(-23).
Think in terms of atoms. That’s what you do.
Big numbers, small constants. When you think of moles,
moderate numbers and moderate value of constants.
We want to ask ourselves, “Is there a microscopic basis
for this equation?” In other words,
once we believe in atoms, do we understand why there is a
pressure at all in a gas? That’s what we’re going to
think about now. So, for this purpose,
we will take a cube of gas. Here it is. This is a cube of side L
by L by L. Inside this is gas and it’s got
some pressure, and I want to know what’s the
value of the pressure. You’ve got to ask yourself,
why is there pressure? Remember, I told you what
pressure means. If you take this face of the
cube, for example, it’s got to be nailed down to
the other faces; otherwise, it’ll just come
flying out because the gas is pushing you out.
The pressure is the force on this face divided by area.
So, somebody inside is trying to get out.
Those guys are the molecules or the atoms, and what they’re
doing is constantly bouncing off the wall,
and every time this one bounces on a wall, its momentum changes
from that to the other one. So, who’s changing the momentum?
Well, the wall is changing the momentum.
It’s reversing it. For example,
if you bounce head-on and go back, your momentum is reversed.
That means you push the wall with some force and the wall
pushes you back with the opposite force.
It’s the force that you exert on the wall that I’m interested
in. I want to find the force on the
wall, say, this particular face. You can find the pressure on
any face. It’s going to be the same
answer. I’m going to take the shaded
face to find the pressure on it. Now, if you want to ask,
what is the force exerted by me on any body, I know the force
has a rate of change of momentum,
because that is d/dt of mv, and m is a
constant, and that’s just dv/dt,
which is ma. I’m just using old F=
ma, but I’m writing it as a rate of change and momentum.
Now, I have N molecules or N atoms,
randomly moving inside the box. Each in its own direction,
suffering collisions with the box, bouncing off like a
billiard ball would at the end of the pool table and going to
another wall and doing it. Now, that’s a very complicated
problem, so we’re going to simplify the problem.
The simplification is going to be, we are going to assume that
one-third of the molecules are moving from left to right.
One-third are moving up and down and one-third are moving in
and out of the blackboard. If at all you make an
assumption that the molecules are simply moving in the three
primary directions, of course you will have to give
equal numbers in these directions.
Nothing in the gas that favors horizontal or vertical.
In reality, of course, you must admit the fact they
move in all directions, but the simplified derivation
happens to give all the right physics,
so I’m going to use that. So, N over three
molecules are going back and forth between this wall,
and this wall. I’m showing you a side view.
The wall itself looks like this. The molecules go back and forth. Next assumption.
All the molecules have the same speed, which I’m going to call
v. That also is a gross and crude
description of the problem, but I’m going to do that anyway
and see what happens. So now, you ask yourself the
following question. Take one particular molecule.
When it hits the wall and it bounces back,
its momentum changes from mv to -mv;
therefore, the change in momentum is 2mv. How often does that change take
place? You guys should think about
that first. How often will that collision
take place? Once you hit the wall here,
you’ve got to go to the other wall and come back.
So, you’ve got to go a distance 2L, and you’re going at a
speed v, the time it takes you is
2L over v. So, ΔP over ΔT
is 2L divided by v.
That gives me mv^(2) over L.
That is the force due to one molecule.
That’s the average force. You realize it’s not a
continuous force. The molecule will hit the wall,
there’s a little force exchange between the two,
then there’s nothing, then you wait until it comes
back and hits the wall again. If that were the only thing
going on, what you would find is the wall most of the time,
has no pressure and suddenly it has a lot of pressure and then
suddenly nothing. But fortunately,
this is not the only molecule. There are roughly 10^(23) guys
pounding themselves against the wall.
So, at any given instant, even if it’s 10^(-5) seconds,
there’d be a large number of molecules colliding.
So, that’s why the force will appear to be steady rather than
a sharp noise. It looked very steady because
somebody or other will be pushing against the wall. This is the force due to one
molecule. The force due to all of them
would be N over 3 times mv^(2) over L. N over 3 because of the
N molecules, a third of them were moving in
this direction. You realize the other two
directions are parallel to the wall.
They don’t apply force on the wall.
To apply force on the wall, you’ve got to be moving
perpendicular to the wall. For example,
if the planes that walls are coming out of the blackboard,
moving in and out of the blackboard doesn’t produce a
force on this wall. That produces a force on the
other two faces. So, as far as any one set of
faces is concerned, in one plane,
only the motion orthogonal to that is going to contribute.
That’s why you have N over 3.
We’re almost done. That’s the average force.
If you want, I can denote average by some
F bar. Then what about the average
pressure? The average pressure is the
average force divided by the area of that face,
which is F over L^(2),
that gives me N over 3, mv^(2) over
L^(3). Now, this is very nice because
L^(3) is just the volume of my box. So, I take the L^(3),
which is equal to the volume of my box,
and I send it to the other side and write it as PV equals
N over 3mv^(2). This is what the microscopic
theory tells you. Microscopic theory says,
if your molecules all have a single speed,
they’re moving randomly in space so that a third of them
are moving back and forth against that wall and this wall,
then this is the product PV.
Experimentally, you find PV=
NkT. So, you compare the two
expressions and out comes one of the most beautiful results,
which is that mv^(2) over 2 is 3 over 2kT.
Now that guy deserves a box. Look what it’s telling you.
It’s a really profound formula. It tells you for the first time
a real microscopic meaning of temperature.
What you and I call the temperature for gas is simply,
up to these factors, 3/2 k,
simply the kinetic energy of the molecules.
That’s what temperature is. If you’ve got a gas and you put
your hand into the furnace and it feels hot,
the temperature you’re measuring is directly the
kinetic energy of the molecules. That is a great insight into
what temperature means. Remember, this is not true if
T is measured in centigrade.
If T were measured in centigrade, our freezing point
of water mv^(2), would vanish.
But that’s not what’s implied. T should be measured
from absolute zero. It also tells you why absolute
zero is absolute. As you cool your gas,
the kinetic energy of molecules are decreasing and decreasing
and decreasing, but you cannot go below not
moving at all, right?
That’s the lowest possible kinetic energy.
That’s why it’s absolute zero. At that point,
everybody stops moving. That’s why you have no pressure.
Now, these results are modified by the laws of quantum
mechanics, but we don’t have to worry about that now.
In the classical physics, it’s actually correct to say
that when the temperature goes to zero, all motion ceases.
Now, this is the picture I want you to bear in mind when you say
temperature. Absolute temperature is a
measure of molecular agitation. More precisely,
up to the constant k, 3/2 k,
the kinetic energy of a molecule is the absolute
temperature. That’s for a gas.
If you took a solid and you say, what happens when I heat
the solid? You have a question?
Yes? Student: [inaudible]
Professor Ramamurti Shankar: You divide by 2
because ½ mv^(2) is a familiar quantity,
namely, kinetic energy. That’s why you divide by 2.
Another thing to notice is that every gas, whatever it’s made
of, at a given temperature has a given kinetic energy because the
kinetic energy per molecule on the left-hand side is dependent
on absolute temperature and nothing else.
So at certain degrees, like 300 Kelvin,
hydrogen kinetic energy would be the same, carbon kinetic
energy would also be the same. The kinetic energy will be the
same, not the velocity. So, the carbon atom is heavier,
it will be moving slower at that temperature in order to
have the same kinetic energy. So, all molecules,
all gases, have a given temperature.
All atoms, let me say, at a given temperature in
gaseous form will have the same kinetic energy [per molecule].
Now, if you have a solid–What’s the difference
between a gas and a solid? In a gas, the atoms are moving
anywhere they want in the box. In a solid, every atom has a
place. If you take a two-dimensional
solid, the atoms look like this. They form a lattice or an array.
That’s because you will find out that, this is more advanced
stuff, that every atom finds itself in a potential that looks
like this. Imagine on the ground you make
these hollows. Low points — low potential;
high points — high potential. Obviously, if you put a bunch
of objects here they will sit at the bottom of these little
concave holes you’ve dug in the ground.
At zero degrees absolute all atoms will sit at the bottom of
their allotted positions; that’ll be a solid at zero
temperature. So in a solid,
everybody has a location. I’ve shown you a
one-dimensional solid, but you can imagine a
three-dimensional solid where in a lattice of three-dimensional
points, there’s an assigned place for
each atom and it sits there. If you heat up that solid now,
what happens is these guys start vibrating.
Now, here is where your knowledge of simple harmonic
motions will come into play. When you take a system in
equilibrium, it will execute simple harmonic motion if you
give it a real kick. If you put it on top of a
hotplate, the atoms in the hot plate will bump into these guys
and start them moving. They will start vibrating.
So, a hot solid is one in which the atoms are making more and
more violent oscillations around their assigned positions.
If you heat them more and more and more, eventually you start
doing this. You go all the way from here to
here; there is nothing to prevent it
from rolling over to the next side.
Once you jump the fence, you know, think of a bunch of
houses, okay? Or a hole in the ground.
You’re living in a hole in the ground, as you get agitated
you’re able to do more and more oscillations so you can roll
over to the next house. Once that happens all hell
breaks loose because you don’t have any reason to stay where
you are. You start going everywhere.
What do you think that is? Student: Melting.
Professor Ramamurti Shankar: Pardon me?
Student: Melting. Professor Ramamurti
Shankar: That’s melting. That’s the definition of
melting. Melting is when you can leap
over this potential barrier, potential energy barrier,
and go to the next site. The next side is just like this
side. If you can jump that fence,
you can jump this one. You go everywhere and you melt.
That’s the process of melting, and once you have a liquid,
atoms don’t have a definite location.
Now, between a liquid and a solid, there is this clear
difference, but a liquid and a vapor is more subtle.
So, I don’t want to go into that.
If you look at a liquid locally, it will look very much
like a solid in the sense that inter-atomic spacing is very
tightly constrained in liquid. Whereas in a solid,
if I know I am here, I know if I go 100 times the
basic lattice spacing, there’ll be another person
sitting there. That’s called long-range order.
In a liquid, I cannot say that. In a liquid,
I can say I am here. Locally, the environment around
me is known, but if you go a few hundred miles,
I cannot tell you a precise location if some other atom will
be there or not. So, we say liquid is
short-range positional order, but not long-range order,
and a gas has no order at all. If I tell you there’s a gas
molecule here, I cannot tell you where anybody
else is because nobody has any assigned location.
Okay. So, this is the picture you
should have of temperature. Temperature is agitated motion.
Either motion in the vicinity of where you are told to sit.
If you’re in a solid a motion all over the box with more and
more kinetic energy. The next thing in this
caricature is that it is certainly not true that a third
of the molecules are moving back and forth.
We know that’s a joke, right? Now, in this room there’s no
reason on earth a third of the molecules are doing this than
others are doing. That’s not approximation.
They’re moving in random directions.
So, if you really got the stomach for it,
you should do a pressure calculation in which you assume
the molecules of random velocities sprinkled in all
directions, and after all the hard work,
turns out you get exactly this answer.
So, that’s one thing I didn’t want to do.
But something I should point out to you is the following.
So, suppose I give you a gas at 300 Kelvin.
You go and you take this formula literally and you
calculate from it a certain ½ mv^(2).
If you knew the mass of the atom, say, it’s hydrogen,
we know the mass of hydrogen. Then, you find the velocity and
you say okay, this man tells me that anytime
I catch a hydrogen atom, it’ll have this velocity at 300
Kelvin. It may have random direction,
but he tells me that’s the velocity square.
Take the square root of that, that’s the velocity.
It seems to us saying the unique velocity to each
temperature. Well, that’s not correct.
Not only are the molecules moving in random directions,
they’re also moving with essentially all possible
velocities. In fact, there are many,
many possible velocities and this velocity I’m getting,
in this formula, is some kind of average
velocity, or the most popular one,
or the most common one. So, if you really go to a gas
and you have the ability to look into it and see for each
velocity, what’s the probability that I get that velocity?
The picture I’ve given you is the probability of zero except
at this one magical velocity controlled by the temperature.
But the real graph looks like this. It has a certain peak.
It likes to have a certain value.
If you know enough about statistics, you know there’s a
most probable value, there’s a median,
there’s a mean value. There are different definitions.
They will all vary by factors of order 1, but the average
kinetic energy will obey this condition.
Yes? Student: [inaudible]
Professor Ramamurti Shankar: It’s not really a
Gaussian because if you draw the nature of this curve,
it looks like v^(2)e to the -mv^(2) over
2kT. That’s the graph I’m trying to
draw here. So, it looks like a Gaussian in
the vicinity of this, but it’s kind of skewed.
It’s forced to vanish at the origin. And it’s not peaked at v
=0. A real Gaussian peak at this
point would be symmetric. It’s not symmetric;
it vanishes here and it vanishes infinity.
So, this is called a Maxwell-Boltzmann distribution.
You don’t have to remember any names but that is the detailed
property of what’s happening in a gas.
So, a temperature does not pick a unique velocity,
but it picks this graph. If you vary your temperature,
look at what you have to do. If you change the number
T here, if you double the value of
T, that means if you double the
value of v^(2) here and there, the graph will look the
same. So, at every temperature there
is a certain shape. If you go to your temperature,
it will look more or less the same, but it may be peaked at a
different velocity if you go to a higher temperature.
Now, this is another thing I want to tell you.
If you took a box containing not atoms but just radiation,
in other words, go inside a pizza oven.
Take out all the air, but the oven is still hot,
and the walls of the oven are radiating electromagnetic
radiation. Electromagnetic radiation comes
in different frequencies, and you can ask how much energy
is contained in every possible frequency range.
You know, each frequency is a color so you know that.
So, how much energy is in the red and how much is in the blue?
That graph also looks like this. That’s a more complicated law
called the Planck distribution. That law also has a shape
completely determined by temperature.
Whereas for atoms, the shape is determined by
temperature as well as the mass of the molecules.
In the case of radiation, it’s determined fully by
temperature and the velocity of light.
You give me a temperature, and I will draw you another one
of these roughly bell-shaped curves.
As you heat up the furnace, the shape will change. So again, a temperature for
radiation means a particular distribution of energies at each
frequency. For a gas it means a
distribution of velocities. Has anybody seen that in the
news lately, you know, or heard about this?
Student: [inaudible] Professor Ramamurti
Shankar: Pardon me? Student: [inaudible]
Professor Ramamurti Shankar: About this
particular graph for radiation. The probability at each
frequency of finding radiation of the frequency in a furnace of
some temperature T. Yes?
Student: [inaudible] Professor Ramamurti
Shankar: No, but in current news.
In the last few years, what people did was the
following. It’s one of the predictions of
the Big Bang theory that the universe was formed some 14 and
a half billion years ago, and in the earliest stages the
temperature of the universe was some incredibly high degrees,
then as it expanded the universe cooled,
and today, at the current size, it has got a certain average
temperature, which is a remnant of the Big
Bang. And that temperature means that
we are sitting in furnace of the Big Bang.
But the furnace has cooled a lot over the billions of years.
The temperature of the universe is around 3 degrees Kelvin.
And the way you determine that is you point your telescope in
the sky. Of course, you’re going to get
light from this star; you’re going to get light from
that star. Ignore all the pointy things
and look at the smooth background, and it should be the
same in all directions. And plot that radiation,
and now they use satellites to plot that, and you’ll get a
perfect fit to this kind of furnace radiation,
called Black Body Radiation. And you read the temperature by
taking that graph and fitting it to a graph like this,
but there’ll be temperature. In the case of light,
this won’t be velocity squared, but it will be the frequency
squared, but read off the temperature
that’ll make this work and that’s what gives you 3.1 or
something. Near 3 degrees Kelvin.
In fact, the data point for that now if you got that in your
lab then you will be definitely busted for fudging your data
because it’s a perfect fit to Black Body Radiation.
One of the most perfect fits to Black Body Radiation is the
background radiation of the Big Bang.
And it’s isotropic, meaning it’s the same in all
directions, and this is one of the predictions of the Big Bang
is that that’ll be the remnant of the Black Body Radiation.
Again, it tells you there’s a sense in which,
if you go to intergalactic space, that is your temperature.
That’s the temperature you get for free.
We’re all living in that heat bath at 3 degrees.
You want more heat, you’ve got to light up your
furnace but this is everywhere in the universe,
that heat left over from creation.
Okay. That’s a very,
very interesting subject. You know, a lot of new physics
is coming out by looking at just the Black Body Radiation because
the radiation that’s coming to your eye left those stars long
ago. So, what you see today is not
what’s happening today. It’s what happened long ago
when the radiation left that part of the universe.
Therefore, we can actually tell something about the universe not
only now, but at earlier periods.
And that’s the way in which we can actually tell whether the
universe is expanding or not expanding or is it accelerating
in its expansion, or you can even say once it was
decelerating and now it’s accelerating.
All that information comes by being able to look at the
radiation from the Big Bang. But for you guys,
I think the most interesting thing is that when you are in
thermal equilibrium, and you are living in a certain
temperature, then the radiation in your world and the molecules
and atoms in your world, will have a distribution of
frequencies and velocities given by that universal graph.
Now in our class, we will simplify life and
replace this graph with a huge peak at a certain velocity by
pretending everybody’s at that velocity.
We will treat the whole gas as if it was represented by single
average number. So, when someone says find the
velocity of molecules, they’re talking about the
average velocity. You know statistically that
it’s the distribution of answers and an average answer.
Because the average is what you and I have to know.
Namely, ½ mv^(2) is 3/2 kT, on average.
Okay. Now, I’m going to study in
detail thermodynamics. So, the system I’m going to
study is the only one we all study, which is an ideal gas
sitting inside a piston. It’s got a temperature,
it’s got a pressure, and it’s got a volume.
And I’m going to plot here pressure and volume and I’m
going to put a dot and that’s my gas.
The state of my gas is summarized by where you put the
dot. Every dot here is a possible
state of equilibrium for the gas.
Remember, the gas, if you look at it under the
hood, is made up of 10^(23) molecules.
The real, real state of the gas is obtained by saying,
giving me 10^(23) locations and 10^(23) velocities.
According to Newton, that’s the maximum information
you can give me about the gas right now,
because with that and Newton’s laws I can predict the future.
But when you study thermodynamics,
you don’t really want to look into the details.
You want to look at gross macroscopic properties and there
are two that you need. Pressure and volume.
Now, you might say, “What about temperature?”
Why don’t I have a third axis for temperature?
Why is there also not a property?
Yes? Student: [inaudible]
Professor Ramamurti Shankar: Yeah.
Because PV=NkT. I don’t have to give you
T, if I know P and V.
There’s not an independent thing you can pick.
You can pick P and V independently.
You cannot pick T. Let me tell you,
by the way, PV=NkT is not a universal law.
It’s the law that you apply to dilute gases.
But we are going to just study only dilute ideal gas.
Ideal gas is one in which the atoms and molecules are so far
apart that they don’t feel any forces between each other unless
they collide. So, here is my gas.
It’s sitting here. Now, what I do,
I had a few weights on top of it.
Three weights. I suddenly pull out one weight.
Throw it out. What do you think will happen?
Well, I think this gas will now shoot up, it’ll bob up and down
a few times. Then after a few seconds,
or a fraction of a second, it’ll settle down with a new
location. By “settle down,” I mean after
a while I will not see any macroscopic motion.
Then the gas has a new pressure and a new volume.
It’s gone from being there to being there. What about in between?
What happened in between the starting and finishing points?
You might say look, if it was here in the beginning
it was there later, it must’ve followed some path.
Not really. Not in this process,
because if you do it very abruptly, suddenly throwing out
one-third of the weights, there’s a period when the
piston rushes up, when the gas is not in
equilibrium. By that, I mean there is no
single pressure you can associate with the gas.
The bottom of the gas doesn’t even know the top is flying off.
It’s at the old pressure. At the top of the gas there’s a
low pressure. So, different parts of the gas
at different pressure, we don’t call that equilibrium.
So, the dot, representing this system,
moves off the graph. It’s off.
It’s off the radar, and only when it has finally
settled down, the entire gas can make up its
mind on what its pressure wants to be;
you put it back here. So, we have a little problem
that we have these equilibrium states, but when you try to go
from one to another you fly off the map.
So, you want to find a device by which you can stay on the
PV diagram as you change the state of the gas,
and that brings us to the notion of what you call a
quasi-static process. A quasi-static process is
trying to have it both ways in which you want to change the
state of the gas, and you don’t want it to leave
the PV diagram. You want it to be always at
equilibrium. So, what you really want to do
is not put in three big fat blocks like this,
but instead take a gas where you have many,
many grains of sand. They can produce the pressure.
Now, remove one grain of sand. It moves a tiny bit and very
quickly settles down. It is again true during the
tiny bit of settling down you didn’t know what it was doing,
but you certainly nailed it at the second location.
You move one grain at a time, then you get a picture like
this and you can see where this is going.
You can make the grain smaller and smaller and smaller and in a
mathematical sense you can then form a continuous line.
That is to say, you perform a process that
leaves the system arbitrarily close to equilibrium,
meaning give it enough time to readjust to the new pressure,
settle down to the new volume, take another grain and another
grain. And in the spirit of calculus,
you can make these changes vanishing so that you can really
then say you did this. Yes?
Student: Are all of these small processes
reversible? Professor Ramamurti
Shankar: Pardon me? Student: Are all of
these small processes reversible?
Professor Ramamurti Shankar: Yes.
Such a process is also called–you can call it
quasi-static but one of the features of that,
it is reversible. You’ve got to be a little
careful when you say reversible. What we mean by “reversible”
is, if I took off a grain of sand and it came from here to
the next dot, and I put the grain back,
it’ll climb back to where it was.
So, you can go back and forth on this.
But now, that’s an idealized process because if you had a
friction, if you had any friction between the piston and
the walls, then if you took out a grain
and it went up, you put the grain back it might
not come back to quite where it is.
Because some of the frictional losses you will never get back.
You cannot put Humpty Dumpty back.
So, most of the time processes are not reversible,
even if you do them slowly, if there is friction.
So, assume it’s a completely frictionless system.
Because if there is friction, there is some heat that goes
out somewhere and some energy is lost somewhere and we cannot
bring it back. If we took a frictionless
piston and on top of it moved it very, very slowly,
you can follow this graph. That’s the kind of
thermodynamic process we’re talking about.
In the old days, when I studied a single
particular of the xy plane, I just said the guy goes
from here to here to there. That’s very easy to study and
there’s no restriction on how quickly or how fast it moved.
Particles have trajectories no matter how quickly they move.
For a thermodynamic system, you cannot move them too fast,
because they are extended and you are having a huge gas a
single number called pressure, so you cannot change one part
of the gas without waiting for all of them to communicate and
readjust and achieve a global value for the new pressure and
you can move gradually. That’s why it takes time to
drag along 10^(23) particles as if they are the single number or
two numbers characterizing them. So, we’ll be studying processes
like this. Now, this is called a state.
Two is a state and one is a state.
Every dot here, that is a state. Now, in every state of the
system, I’m going to define a new variable,
which is called a quantity called U,
which stands for the internal energy of the gas. Internal energy is simply the
kinetic energy of the gas molecules.
For solids and liquids, there’s a more complicated
formula. For the gas,
internal energy is just the kinetic energy.
And what is that? It is 3/2 kT per
molecule times N. I’m sorry, 3/2 Nk, yeah.
3/2 kT times that. Or we can write it as 3/2
nRT. But nRT is PV.
You can also write it as 3/2 PV, so internal energy is
just 3/2 PV. That means at a given point on
the PV diagram, you have a certain internal
energy. If you are there,
that’s your internal energy. Take there-halves of PV
and that’s the energy and that’s literally the kinetic energy of
all the molecules in your box. So, now I’m ready to write down
what’s called the First Law of Thermodynamics that talks about
what happens if you make a move in the PV plane from one
place to another place. If you go from one place to
another place, your internal energy will
change from U_1 to U_2.
Let’s call it ΔU. We want to ask what causes the
internal energy of the gas to change.
So, you guys think about it now. Now that you know all about
what’s happening in the cylinder, you can ask how I will
change the energy? Well, if you wanted to change
the energy of a system, there are two ways you can do
it. One is you can do work on the
gas. Another thing is you can put
the gas on a hotplate. If you put it on hotplate,
we know it’s going to get hotter.
If it gets hotter, temperature goes up.
If temperature goes up, the internal energy goes up.
So, there are two ways to change the energy of a gas.
The first one we call heat input.
That just means put it on something hotter and let the
thing heat it up. Temperature will go up.
Notice that the internal energy of an ideal gas depends only on
the temperature. That’s something very,
very important. I mention it every time I teach
the subject and some people forget and lose a lot of points
needlessly. So, I’ll say it once more with
feeling. The energy of an ideal gas
depends only on the temperature. If the temperature is not
changed; energy has not changed.
So, try to remember that for what I do later.
So, the change of the gas, this cylinder full that I put
some weights on top and I’ve got gas inside,
it can change either because I did, I put in some heat,
or the gas did some work. By that, I mean if the gas
expands by pushing out against the atmosphere,
then it was doing the work and ΔW is the work done by
the gas. That’s why it comes to the
minus sign, because it’s the work done by the gas.
If you do work, you lose energy. So, what’s the formula for work
done? Let’s calculate that.
If I’ve got a piston here, it’s the force times the
distance. But the force is the pressure
times the area times the distance.
Now, you guys should know enough geometry to know the area
of the piston times the distance it moves is the change in the
volume. So, we can write it as P
times dV. That leads to this great law.
Let me write it on a new blackboard because we’re going
to be playing around with that law.
This is law number one. The change in the internal
energy of a system is equal to ΔQ – PΔV. What does it express?
It expresses the Law of Conservation of Energy.
It says the energy goes up, either because you pushed the
piston or the piston pushed you; then you decide what the
overall sign is, or you put it on a hotplate.
We are now equating putting it on a hotplate as also equivalent
to giving it energy, because we identify heat as
simply energy. So, if you took the piston and
you nailed the piston so it cannot move, and you put it on a
hotplate, PdV part will vanish
because there is no ΔV. That’s the way of heating it,
it is called ΔQ. Another thing you can do is
thermally isolate your piston so no heat can flow in and out of
it, and then you can either have
the volume increase or decrease. If the gas expanded,
ΔV is positive and the PΔ – PΔV is negative,
and the ΔU would be negative;
the gas will lose energy. That’s because the molecules
are beating up on the piston and moving the piston.
Remember, applying a force doesn’t cost you anything.
But if the point of application moves, you do work.
And who’s going to pay for it, the gas?
It’ll pay for it through its loss of internal energy.
Conversely, if you push down on the gas, ΔV will be
negative and this will become positive and the energy of the
gas will go up. So, there are two ways to
change the energy of these molecules.
In the end, all you want is you want the molecules to move
faster than before. One is to put them on a
hotplate where there are fast-moving molecules.
When they collide with the slow-moving molecules,
typically the slow one’s a little more faster and the fast
one’s a little more slower and therefore will be a transfer of
kinetic energy. Or when you push the piston
down, you can show when a molecule collides with a moving
piston. It will actually gain energy.
So, that’s how you do work. That’s the first law. So, let us now calculate the
work done in a process where a gas goes from here to here on an
isotherm. Isotherm is a graph of a given
temperature. So, this is a graph P
times V equal to constant, because PV=
nRT. If T is constant,
PV is a constant, it’s the rectangular hyperbola.
The product of the x and y coordinates is
constant, so when the x coordinate vanished,
the y will go to infinity.
y coordinate vanishes, x will go to infinity.
So, you want to take your gas for a ride from here to here.
Throughout it’s at a certain temperature T.
What work is done by you? That’s a very nice
interpretation. The work done by you is the
integral of PdV. But what is integral of
PdV? That’s P,
and that’s dV. Pdv is that shaded
region. In other words,
if you just write PdV it makes absolutely no sense.
If you go to a mathematician and say, “Please do the integral
for me!” can the mathematician do this?
What’s coming in the way of the mathematician actually doing the
integral? What do you have to know to
really do an integral? Student: You have to
know the function. Professor Ramamurti
Shankar: You have to know the function.
If you just say P, we’ll say maybe P is a
constant, in which case I’ll pull it out of the integral.
But for this problem, because PV is
nRT, and T is a constant,
P is nRT divided by V, and that’s the
function that you would need to do the integral,
and if you did that you will find there’s nRT.
All of them are constants. They come out of the integral,
dv over V, and integrate from the initial
volume, the final volume. And you guys know this is a
logarithm, and the log of upper minus log of lower is the log of
the ratio. And this gives me nRT
ln (V_2 /V_1).
So, we have done our first work calculation.
When the gas goes on an isothermal trajectory from start
to finish, from volume V_1 to volume
V_2, the work done,
this is the work done by the gas.
You can all see that gas is expanding and that’s equal to
this shaded region. By the way, I mention it now,
I don’t want to distract you, but suppose later on I make it
go backwards like this, part of the way.
The work done on the going backwards part is this area,
but with a minus sign. I hope you will understand,
if you go to the right the area’s considered positive.
If you go to the left, the area is considered
negative. If you do the integral and put
the right limit, you’ll get the right answer.
But geometrically, the area under the graph in the
PV diagram is the work done if you’re moving the
direction of increasing volume. If you would decrease the
volume, for example, if you just went back from
here, the area looks the same but the work done is considered
negative. You don’t have to think very
hard. If you do the calculation going
backwards, you will get a ln of
V_1 over V_2.
That’ll automatically be the negative of the log of
V_2 over V_1.
But geometrically, the area under the graph is the
work, if you are going to the right.
Yes? Student: What determines
the shape of the curve that links the first state to the
second state? Professor Ramamurti
Shankar: Oh, this one?
Student: Mmm-hmm. Professor Ramamurti
Shankar: This’ll be a graph, PV equal to essentially
a constant. So, you take your gas,
you see how many moles there are.
You know R, you know the temperature,
you promised not to change the temperature.
So, you’ll move on a trajectory so that the product PV
never changes. And in any xy plane,
if you draw a graph where the product xy doesn’t change
it’ll have this shape called a “rectangular hyperbola.”
It just means, whenever one increases,
the other should decrease, keeping the product constant.
That’s why P is proportional to the reciprocal
of V when you do the integral.
Very good. So, this is now the work done
by the gas. What is the heat input?
The heat input is a change in internal energy minus the work
done. Let me see.
The law was ΔU=ΔQ – ΔW.
Yeah, let’s go back to this law. In this problem,
ΔW is what I just calculated, nRT,
whatever the log, V_2 over
V_1. What is ΔQ?
How much heat has been put into this gas?
How do I find that? Student: Take out the
T? Professor Ramamurti
Shankar: Pardon me? Student: You take out
the T? Professor Ramamurti
Shankar: For the heat input you mean?
Yeah, you can use mc ΔT, but you don’t have to
do anymore work. By that, I mean you don’t have
to do any more cerebration. What can you do with this
equation to avoid doing further calculations?
Do you know anything else? Yes?
Student: [inaudible] Professor Ramamurti
Shankar: Yes. This is what I told you is the
fact that people do not constantly remember,
but you must. This gas did not change its
temperature. Go back to equation number
whatever I wrote down. U=3/2 nRT or
something. T doesn’t change,
U doesn’t change. That means the initial internal
energy and final internal energy are the same because initial
temperature and final temperature are the same.
So, this guy has to be zero. That means ΔQ is the
same as ΔW in this particular case.
Yes? Student: [inaudible]
Professor Ramamurti Shankar: When you say mc
ΔT, you’ve got to be careful of what formula you want
to use. I’ll tell you why you cannot
simply use mc ΔT. If you’ve got a solid and you
use mc ΔT, that is correct,
because when you heat the solid, the heat you put in goes
into heating up the solid. Maybe let’s ask the following
question. His question is the following.
You’re telling me you put heat into a gas, right?
And you say temperature doesn’t go up.
How can that possibly be? I always thought when I put
heat into something, temperature goes up.
That’s because you were thinking about a solid,
where if you put in heat it’s got to go somewhere and,
of course, temperature goes up. What do you think is happening
to the gas here? Think of the piston and weight
combination. When I want to go along this
path from here to here, you can ask yourself where is
the heat input and where is the change in energy,
and why is there no change in temperature?
If you take a piston like this, if you want to increase the
volume, you can certainly take off a grain of sand,
right? If you took the grain of sand
and the piston will move up, it will do work and it actually
will cool down, but that’s not what you’re
doing. You are keeping it on a
hotplate at a certain temperature so that if it tries
to cool down, heat flows from below to above
maintaining the temperature. So, what the gas is doing in
this case is taking heat energy from below and going up and
working against the atmosphere above.
It takes in with one hand and gives out to the other,
without changing its energy. So, when you study specific
heat, which is my next topic, you’ve got to be a little more
careful when you talk about specific heats of gases,
and I will tell you why. There is no single thing called
specific heat for a gas. There are many,
many definitions depending on the circumstances.
But I hope you understand in this case;
you’ve got to visualize this. It’s not enough to draw
diagrams and draw pictures. What did I do to the cylinder
to maintain the temperature and yet let it expand?
Expansion is going to demand work on part of the gas.
That’s going to require a loss of energy unless you pump in
energy from below. So, what I’ve done is that I
take grain after grain, so that the pressure drops and
the volume increases, but the slight expansion would
have cooled it slightly but the reservoir from below brings it
back to the temperature of the reservoir.
So, you prop it up in temperature.
So, we draw the picture by saying the gas went from here to
here, and we usually draw a picture like this and say heat
flowed into the system during that process.
Alright, now I’ll come to this question that was raised about
specific heat. Now, specific heat,
you always say is ΔQ over ΔT or ΔT
divided by the mass of the substance.
Now, it turns out that for a gas, you’ve already seen that
what you want to count is not the actual mass,
but the moles. Because we have seen at the
level of the ideal gas law, the energy is controlled by not
simply the mass, but by the moles.
Because every molecule gets a certain amount of energy,
namely 3/2 kT, and you just want to count the
number of molecules, or the number of moles.
Now, there are many, many ways in which you can pump
in heat into a gas and heat it up and see how much heat it
takes. But let’s agree that we will
take one mole from now on and not one kilogram.
Not one kilogram. We’ll find out if you do it
that way, the answer doesn’t seem to depend on the gas.
That’s the first thing. Take a mole of some gas and
call the specific heat as the energy needed to raise the
temperature of one mole by one degree.
So, this should not be m. This should be the number of
moles. If you take one mole,
you can say okay, one mole of gas I was told has
energy U=3/2 RT. Because it was there-halves
nRT but n is one mole.
Now, you want to put in some heat, and you really want the
ΔQ over ΔT, so I will remind you that
ΔQ is ΔU + PΔv. The heat input into a gas is
the change of energy plus P Δv.
And that’s just from the first law.
So, if I’m going to divide ΔQ by ΔT,
there’s a problem here. Did you allow the volume to
change or did you not allow the volume to change?
That’s going to decide what the specific heat is.
In other words, when a solid is heated,
it expands such a tiny amount, we don’t worry about the work
done by the expanding solid against the atmosphere.
But for a gas, when you heat it,
the volume changes so much that the work it does against the
external world is non-negligible.
Therefore, the specific heat is dependent on what you allow the
volume term to do. So, there’s one definition of
specific heat called C_V,
and C_V is the one at constant volume.
You don’t let the volume change. In other words,
you take the piston and you clamp it.
Now, you pump in heat from below by putting it on a
hotplate. All the heat goes directly to
internal energy. None of that is lost in terms
of expansion. So, ΔV is zero.
In that case, ΔQ over ΔT at
constant volume, we denote that in this fashion,
at constant volume, this term is gone,
and it just becomes ΔU over ΔT.
That’s very easily done. ΔU over ΔT is
3/2 R. So, the specific heat of a gas
at constant volume is 3 over 2R.
When I studied solids, I never bother about constant
volume because a change in the volume of a solid is so
negligible when it’s heated up, it’s not worth specifying that
it was a constant volume process.
But for a gas, it’s going to matter whether it
was constant volume or not. Then, there’s a second specific
heat people like to define. That’s done as follows.
You take this piston. You have some gas at some
pressure. You pump in some heat but you
don’t clamp the piston. You let the piston expand any
way it wants at the same pressure.
For example, if it’s being pushed down by
the atmosphere, you let the piston move up if
it wants to, maintaining the same pressure.
Well, if it moves up a little bit, then the correct equation
is the heat that you put in is the change in internal energy
plus P times ΔV, where now P is some
constant pressure, say the atmospheric pressure,
ΔV is the change in volume.
So, ΔQ needed now will be more, because you’re pumping
in heat from below and you’re losing energy above because
you’re letting the gas expand. Because you were letting the
pressure be controlled from the outside at some fixed value.
So now, ΔQ–this ΔU will be 3 over
2RΔT. Now, what’s the change in
P times ΔV? Here is where you should know
your calculus. The P times change in
V is the same as the change in PV,
if P is a constant. Right?
Remember long back when I did rate of change of momentum is
d/dt of mv, it’s m times
dv/dt, because m doesn’t
change. You can take it inside the
change. But now we use PV=RT.
I’m talking about one mole. PV=RT.
That’s a change in the quantity RT, R is a
constant, that’s R times ΔT so I put in here
R times ΔT. This is the ΔQ at
constant pressure. So, the specific heat of
constant pressure is ΔQ over ΔT,
keeping the pressure constant. You divide everything by
ΔT you get 3 over 2R, plus another
R, which is 5 over 2R. So, the thing you have to
remember, what I did in the end, is that a gas doesn’t have a
single specific heat. If we just say,
put in some heat and tell me how many calories I need to
raise the temperature, that’s not enough.
You have to tell me whether in the interim, the gas was fixed
in its volume, or changed its volume,
or obeyed some other condition. The two most popular conditions
people consider are either the volume cannot change or the
pressure cannot change. If the volume cannot change,
then the change in the heat you put in goes directly to internal
energy, from the First Law of Thermodynamics.
That gives you a specific heat of 3 over 2R.
If the pressure cannot change, you get 5 over 2R.
You can see C_P is bigger
than C_V because when you let the piston
expand, then not all the heat is going
to heat the gas. Some of it is dissipated on top
by working against the atmosphere.
Then, notice that I’ve not told you what gas it is.
That’s why the specific heat per mole is the right thing to
think about because then the answer does not depend on what
particular gas you took. Whether it’s hydrogen or
helium, they all have the same specific heat per mole.
They won’t have the same specific heat per gram,
right? Because one gram of helium and
one gram of hydrogen don’t have the same number of moles.
So, you have to remember that we’re talking about moles.
The final thing I have to caution you–very,
very important. This is for a monoatomic gas. This is for a gas whose atom is
the gas itself. It’s a point.
Its only energy is kinetic energy.
There are diatomic gases, by two of them [atoms]
joined together, they can form a dumbbell or
something; then the energy of the dumbbell
has got two parts, as you learned long ago.
It can rotate around some axis and it can also move in space.
Then the internal energy has also got two parts.
Energy due to motion of the center of mass and energy due to
rotation. Some molecules also vibrate.
So, there are lots of complicated things,
but if you got only one guy, or one atom,
whatever its mass is, it cannot rotate around itself
and it cannot vibrate around itself,
so those energies all disappear. So, we have taken the simplest
one of a monoatomic gas, a gas whose fundamental entity
is a single atom rather than a complicated molecule.
And that’s all you’re responsible for.
I’ll just say one thing. C_P over
C_V, I want to mention it before you
run off to do your homework. I don’t know if it comes up.
It’s called γ, that’s five-third for a
monoatomic gas. You can just take the ratio of
the numbers. If in some problem you find
γ is not five-thirds, do not panic.
It just means it’s a gas which is not monoatomic.
If it’s not monoatomic, these numbers don’t have
exactly those values. We don’t have to go beyond that.
You just have to know there’s a ratio γ,
which is five-thirds in the simplest case,
but in some problem, somewhere in your life,
you can get a γ which is not five-thirds.