# First law of thermodynamics / internal energy | Thermodynamics | Physics | Khan Academy

I’ve now done a bunch of videos
on thermodynamics, both in the chemistry and the
physics playlist, and I realized that I have yet to give
you, or at least if my memory serves me correctly, I
have yet to give you the first law of thermodynamics. And I think now is as
good a time as any. The first law of
thermodynamics. And it’s a good one. It tells us that energy– I’ll
do it in this magenta color– energy cannot be created or
destroyed, it can only be transformed from one
form or another. So energy cannot be created or
destroyed, only transformed. So let’s think about a couple
of examples of this. And we’ve touched on this when
we learned mechanics and kinetics in our physics
playlist, and we’ve done a bunch of this in the chemistry
playlist as well. So let’s say I have some rock
that I just throw as fast as I can straight up. Maybe it’s a ball
of some kind. So I throw a ball straight up. That arrow represents its
velocity vector, right? it’s going to go
up in the air. Let me do it here. I throw a ball and it’s going
to go up in the air. It’s going to decelerate
due to gravity. And at some point, up here, the
ball is not going to have any velocity. So at this point it’s going to
slow down a little bit, at this point it’s going to slow
down a little bit more. And at this point it’s going
to be completely stationary and then it’s going to start
accelerating downwards. In fact, it was always
accelerating downwards. It was decelerating upwards,
and then it’ll start accelerating downwards. So here its velocity will
look like that. And here its velocity
will look like that. Then right when it gets back
to the ground, if we assume negligible air resistance, its
velocity will be the same magnitude as the upward but
in the downward direction. So when we looked at this
example, and we’ve done this tons in the projectile motion
videos in the physics playlist, over here we said,
look, we have some kinetic energy here. And that makes sense. I think, to all of us, energy
intuitively means that you’re doing something. So kinetic energy. Energy of movement,
of kinetics. It’s moving, so it has energy. But then as we decelerate up
here, we clearly have no kinetic energy, zero
kinetic energy. So where did our energy go? I just told you the first law of
thermodynamics, that energy cannot be created
or destroyed. But I clearly had a lot of
kinetic energy over here, and we’ve seen the formula for that
multiple times, and here I have no kinetic energy. So I clearly destroyed kinetic
energy, but the first law of thermodynamics tells me
that I can’t do that. So I must have transformed
that kinetic energy. I must have transformed
that kinetic energy into something else. And in the case of this ball,
I’ve transformed it into potential energy. So now I have potential
energy. And I won’t go into the math of
it, but potential energy is just the potential to turn into
other forms of energy. I guess that’s the easy
way to do it. But the way to think about it
is, look, the ball is really high up here, and by virtue of
its position in the universe, if something doesn’t stop it,
it’s going to fall back down, or it’s going to be converted
into another form of energy. Now let me ask you
another question. Let’s say I throw this ball up
and let’s say we actually do have some air resistance. So I throw the ball up. I have a lot of kinetic
energy here. Then at the peak of where the
ball is, it’s all potential energy, the kinetic energy
has disappeared. And let’s say I have
air resistance. So when the ball comes back
down, the air was kind of slowing it down, so when it
reaches this bottom point, it’s not going as fast
as I threw it. So when I reach this bottom
point here, my ball is going a lot slower than I threw
it up to begin with. And so if you think about what
happened, I have a lot of kinetic energy here. I’ll give you the formula. The kinetic energy is the mass
of the ball, times the velocity of the ball,
squared, over 2. That’s the kinetic
energy over here. And then I throw it. It all turns into potential
energy. Then it comes back down, and
turns into kinetic energy. But because of air resistance,
I have a smaller velocity here. I have a smaller velocity
than I did there. Kinetic energy is only dependent
on the magnitude of the velocity. I could put a little absolute
sign there to show that we’re dealing with the magnitude
of the velocity. So I clearly have a lower
kinetic energy here. So lower kinetic energy here
than I did here, right? And I don’t have any potential
energy left. Let’s say this is the ground. We’ve hit the ground. So I have another conundrum. You know, when I went from
kinetic energy to no kinetic energy there, I can go
to the first law and say, oh, what happened? And the first law says, oh,
Sal, it all turned into potential energy up here. And you saw it turned into
potential energy because when the ball accelerated back down,
it turned back into kinetic energy. But then I say, no, Mr. First
Law of Thermodynamics, look, at this point I have no
a lot of kinetic energy. Now at this point, I have no
potential energy once again, but I have less kinetic
energy. My ball has fallen at
a slower rate than I threw it to begin with. And the thermodynamics
says, oh, well that’s because you have air. And I’d say, well I do
have air, but where did the energy go? And then the first law of
thermodynamics says, oh, when your ball was falling– let
me see, that’s the ball. Let me make the ball yellow. So when your ball was falling,
it was rubbing up against air particles. It was rubbing up against
molecules of air. And right where the molecules
bumped into the wall, there’s a little bit of friction. Friction is just essentially,
a little bit faster. And essentially, if you think
about it, if you go back to the macrostate/ microstate
problem or descriptions that we talked about, this ball is
essentially transferring its kinetic energy to the molecules
of air that it rubs up against as it falls
back down. And actually it was doing it
on the way up as well. And so that kinetic energy that
you think you lost or you destroyed at the bottom, of
here, because your ball’s going a lot slower, was actually
transferred to a lot of air particles. It was a lot of– to a bunch
of air particles. Now, it’s next to impossible to
measure exactly the kinetic energy that was done on each
individual air particle, because we don’t even know what
their microstates were to begin with. But what we can say is, in
general I transferred some heat to these particles. I raised the temperature of
the air particles that the ball fell through by rubbing
those particles or giving them kinetic energy. Remember, temperature is just
a measure of kinetic– and temperature is a macrostate or
kind of a gross way or a macro way, of looking at the
kinetic energy of the individual molecules. It’s very hard to measure each
of theirs, but if you say on average their kinetic energy
is x, you’re essentially giving an indication
of temperature. So that’s where it went. It went to heat. And heat is another
form of energy. So that the first law
of thermodynamics says, I still hold. You had a lot of kinetic energy,
turned into potential, that turned into less
kinetic energy. And where did the
remainder go? It turned into heat. Because it transferred that
kinetic energy to these air particles in the surrounding
medium. Fair enough. So now that we have that out of
the way, how do we measure the amount of energy that
something contains? And here we have something
called the internal energy. The internal energy
of a system. Once again this is a macrostate,
or you could call it a macro description
of what’s going on. This is called u for internal. The way I remember that is that
the word internal does not begin with a U. U for internal energy. Let me go back to my example–
that I had in the past, that I did in our previous video, if
you’re watching these in order– of I have, you know,
some gas with some movable ceiling at the top. That’s its movable ceiling. That can move up and down. We have a vacuum up there. And I have some gas in here. The internal energy literally is
all of the energy that’s in the system. So it includes, and for our
purposes, especially when you’re in a first-year chemistry
course, it’s the kinetic energy of all the
atoms or molecules. And in a future video, I’ll
actually calculate it for how much kinetic energy is
there in a container. And that’ll actually be our
internal energy plus all of the other energy. So these atoms, they have some
kinetic energy because they have some translational motion,
if we look at the microstates. If they’re just individual
atoms, you can’t really say that they’re rotating, because
what does it mean for an atom to rotate, right? Because its electrons are just
jumping around anyway. So if they’re individual atoms
they can’t rotate, but if they’re molecules they can
rotate, if it looks something like that. There could be some rotational
energy there. It includes that. If we have bonds– so I
just drew a molecule. The molecule has bonds. Those bonds contain
some energy. That is also included in
the internal energy. If I have some electrons, let’s
say that this was not a– well I’m doing it using a
gas, and gases aren’t good conductors– but let’s say
I’m doing it for a solid. So I’m using the wrong tools. So let’s say I have
some metal. Those are my metal– let me do
more– my metal atoms. And in that metal atom, I have, a
bunch of electrons– well that’s the same color– I have
a bunch of– let me use a suitably different color–
I have a bunch of electrons here. And I have fewer here. So these electrons really
want to get here. Maybe they’re being stopped for
some reason, so they have some electrical potential. Maybe there’s a gap here, you
know, where they can’t conduct or something like that. Internal energy includes
that as well. That’s normally the scope out
of what you’d see in a first-year chemistry class. But it includes that. It also includes literally
every form of energy that exists here. It also includes, for example,
in a metal, if we were to heat this metal up they start
vibrating, right? They start moving left and
right, or up or down, or in every possible direction. And if you think about a
molecule or an atom that’s vibrating, it’s going from here,
and then it goes there, then it goes back there. It goes back and forth, right? And if you think about what’s
happening, when it’s in the middle point it has a lot of
kinetic energy, but at this point right here, when it’s
about to go back, it’s completely stationary for
a super small moment. And at that point, all
of its kinetic energy is potential energy. And then it turns into
kinetic energy. Then it goes back to potential
energy again. It’s kind of like a
pendulum, or it’s actually harmonic motion. So in this case, internal
energy also includes the kinetic energy for the molecules
that are moving fast. But it also includes the
potential energies for the molecules that are vibrating,
they’re at that point where they don’t have kinetic
energy. So it also includes
potential energy. So internal energy is literally
all of the energy that’s in a system. And for most of what we’re going
to do, you can assume that we’re dealing with
an ideal gas. Instead of, it becomes a lot
more complicated with solids, and conductivity, and vibrations
and all that. We’re going to assume we’re
dealing with an ideal gas. And even better, we’re going to
assume we’re dealing with a monoatomic ideal gas. And maybe this is just
helium, or neon. One of the ideal gases. They don’t want to bond
with each other. They don’t form molecules
with each other. Let’s just assume that
they’re not. They’re just individual atoms.
And in that case, the internal energy, we really can simplify
to it being the kinetic energy, if we ignore all
of these other things. But it’s important to realize,
internal energy is everything. It’s all of the energy
inside of a system. If you said, what’s the
energy of the system? Its internal energy. So the first law of
thermodynamics says that energy cannot be created or
destroyed, only transformed. So let’s say that internal
energy is changing. So I have this system, and
someone tells me, look, the internal energy is changing. So delta U, that’s just a
capital delta that says, what is the change an internal
energy? It’s saying, look, if your
internal energy is changing, your system is either having
something done to it, or it’s doing something to
someone else. Some energy is being
transferred to it or away from it. So, how do we write that? Well the first law of
thermodynamics, or even the definition of internal energy,
says that a change in internal energy is equal to heat added to
the system– and once again a very intuitive letter for
convention is to use Q for heat. The letter h is reserved for
enthalpy, which is a very, very, very similar
concept to heat. We’ll talk about that maybe
in the next video. It’s equal to the heat added to
the system, minus the work done by the system. And you could see this
multiple ways. Sometimes it’s written
like this. Sometimes it’s written that the
change in internal energy is equal to the heat added to
the system, plus the work done on the system. And this might be very
confusing, but you should just always– and we’ll really kind
of look at this 100 different ways in the next video. And actually this
is a capital U. Let me make sure that I write
that as a capital U. But we’re going to do it
100 different ways. But if you think about it, if
I’m doing work I lose energy. I’ve transferred the energy
to someone else. So this is doing work. Likewise, if someone is giving
me heat that is increasing my energy, at least to me these
are reasonably intuitive definitions. Now if you see this, you say,
OK, if my energy is going up, if this is a positive thing, I
either have to have this go up, or work is being
done to me. Or energy is being transferred
into my system. I’ll give a lot more examples of
what exactly that means in the next video. But I just want to make
you comfortable with either of these. Because you’re going to see
them all the time, and you might even get confused
even if your teacher uses only one of them. But you should always do
this reality check. When something does work, it
is transferring energy to something else, right? So if you’re doing work, it’ll
take away, this is taking away, your internal energy. Likewise, heat transfer is
another way for energy to go from one system to another, or
from one entity to another. So if my total energy is going
up, maybe heat is being added to my system. If my energy is going down,
either heat is being taken away from my system, or I’m
doing more work on something. I’ll do a bunch of examples
with that. And I’m just going to leave you
with this video with some other notation that
you might see. You might see change in internal
energy is equal to change– let me write it again–
change in internal energy, capital U. You’ll sometimes see it as,
they’ll write a delta Q, which kind of implies change
in heat. But I’ll explain it in a future
video why that doesn’t make a full sense, but you’ll
see this a lot. But you can also view this as
the heat added to the system, minus the change in work,
which is a little non-intuitive because when you
of energy. So when you talk about change
in transfer it becomes a little– So sometimes a delta
work, they just mean this means that work done
by a system. So obviously if you have some
energy, you do some work, you’ve lost that energy, you’ve
given it to someone else, you’d have a
minus sign there. Or you might see it written like
this, change in internal energy is equal to heat added–
I won’t say even this kind of reads to me
as change in heat. I’ll just call this the heat
added– plus the work done onto the system. So this is work done to, this
is work done by the system. Either way. And you shouldn’t even memorize
this, you should just always think about
it a little bit. If I’m doing work I’m going
to lose energy. If work is done to me I’m
going to gain energy. If I lose heat, if this is a
negative number, I’m going to lose energy. If I gain heat I’m going
to gain energy. Anyway, I’ll leave you there
for this video, and in the next video we’ll really try to
digest this internal energy formula 100 different ways.

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BryceSH1992 says:

wow. Its week tw and im still confused but now i understand. Thanks very much

toto11132 says:

Matter is in fact   the density between the protons and electrons the more space out the atoms are the more less density you have  the more Matter becomes  less hard, like steel for example his energy is very compact because Atoms are very close to each other

Martian says:

So someone explain to me food for knowledge or whatever, why when the ball is thrown in the air and when it comes back down its now called potential energy instead of energy dying out and please dont just say "energy can't be created or destroy"?..why is the ball coming back down consider energy still? What makes that energizing in anyway? 🙁

Belin Tilija says:

Anubhav Singh says:

I LOVE YOUR VOICE….I thought you are from Pakistan or India?

Ian Delos Angel says:

Falcon X says:

Thank you khan, you are the man!

Nathan Clark says:

So it was said that atoms don't really have rotational energy but molecules potentially do bc of sigma bonds that are able to rotate.  However, atoms have atomic spin.  Doesn't that translate into rotational energy?  Was this an accidental omission or do atoms also have rotational energy?  Much gratitude for your videos!

Flying Man says:

HALLOOO GR-9 INDUSTRY !!!!!!!!!!!!!!!!!!!

Smail Waltit says:

thank you for this interesting video

Smail Waltit says:

very few teachers uses this concrete method,,, talented

alex cha says:

check out this thermochem review tool! It is a music video covering the essential topics of thermochem.  WHile very entertaining, it is very informative.  YOULL RERET IT IF U DONT WATCH!!! subscribe!!

Eli Doubleday says:

Any else here because of cloud cult? No? Just me? Ok.

kendo512 says:

I've been watching these videos for close to 4 years now. I love how you can tell the age of his videos by the resolution of the writing. The newer ones are so much more crisp.

Blu Jacket says:

I'm here because of Rick&Morty

The Card says:

Khan post too many videos. Coolest people ever

Mukesh kesharwani says:

very boring

john pia gan says:

THIS VIDEO WAS VERY INFORMATIVE.CAN YOU PLEASE KICK THE ASS OF MY PROFESSOR

Grautskalle says:

sal i fuken love you bro

eragon2121 says:

U for internal energy. The way I remember that is internal does not start with a U.

bontha venkata jayanth says:

When the ball is in motion the mass also changes.
E=MCsquare
Energy increased so to balance it mass shound increase as C which is speed of light in vacuum is constant.

iTz JackiE says:

can u apply for the physics/physical chemistry job here at Mississippi valley state university. you are more than welcome to show my suck ass professor how this teaching thang really suppose to be

Harvey says:

This is Amazing

Sun Kaur says:

good one

Raj Harsh says:

That Is like the first law of everything.

Kevin Gomez says:

Thank you so much

Clinton Raubenheimer says:

Am I wrong in saying that the ball is a bad example since the ball will only ever reach terminal velocity on its descent?

Brassdogs Barking says:

"potential energy"? how is that real and not a construct!? can we interact with "potential energy"?

Sakshi Agarwal says:

Thankyou so much sir you are just amazing.

Jean Passepartout says:

why tf does he love magenta so much??

An Humble Messenger of the Law of One says:

Teach us Dewey Larson's theory of space and time. Instead of leading us astray.

Maximus Prime says:

thanks for taking something so simple and making it complicated Einstein. Everything is made of energy. E=m©2 if I burn a piece of wood, the wood gets broken down into more fundamental elements but every single molecule that existed in the wood still exist but in different states.

Sandip Rav says:

😎👌👌👌👍👍👍

change in "Q" doesn't make any sense because heat is added to system from surrounding and is constant (doesn't change)??

Marella Indira Chowdary says:

If you guys don't mind could you please define ENERGY i.e definition

JDR Burk says:

Great information and delivery, but why does his pen look soo pixelated and not smooth like other vids…?

Deependra Verma says:

Why shouldn't be air resistance working when you throw the ball with more KE?

Moon Star says:

Thermodynamics An Engineering Approach – ed5 – Cengel, Boles – Book + Solution ; http://turbobit.net/v4rj2vrih5mh.html

Lenin says:

what app or program do they use for these videos?

Asim Rashid says:

from where kinetic comes from ?although the participial is at ground state the is no motion.
kinetic energy is due to the motion of particles /mass??

Nepal 16 yrs astronomists group says:

Cant be understandsble.WTF.

Sarah Jean Brown says:

does this guy just know everything. no matter what class im struggling with, he's got something up his sleeve lol

Onanuga Damilare says:

hi khan academy does it mean in a thermodynamic cycle change in internal energy is zero

St. Francis says:

Chris Guillen says:

What is air

Demiurge says:

"no Mr first law of thermodynamics '' this should be a line in a Neil Gaiman book

Chris Guillen says:

Don't you have air resistance throwing the ball up into the air as well (as it falling downward)?

Can someone explain to me why there is more kinetic energy when the ball is thrown upwards than when it is falling downward?

I would have thought because there is nothing opposing gravity's negative acceleration then the kinetic energy would be greater. Though you say there IS opposition and that it is air resistance, I wonder why you say there isn't any as the ball is thrown upward..

Caroline Marwan says:

Thank you so much! Extremely helpful 👌🏻

Pawan Rangile says:

r u muslim?

Jenny says:

Khan, you're the best! Literally life saver for my exam in 3 days.

MRO says:

It's it's it's….it's very helpful 😉

StarryGlobe089 says:

''This is the U for internal energy. The way I remembar that is that the word internal does not begin with a U.''
Seems clear

andrew hastings says:

Where did the remaining kinetic energy go after the ball hit the ground?

Kyle Ditzenberger says:

Khan academy should be getting about 3% of every single Chem or Physics professors salary lol

JuJu ReFeReNcE says:

sooooo that means machines of perpetual movement will stop working at some time?

morty can explain this

Akash Deepak says:

This not the first law it is law of conservation of energy. First law of thermodynamics states that for the closed system algebraic summation of work transfer is equal to the algebraic summation of the heat transfered….

Jeremiah Fowler says:

Snarky, the Cat says:

Morty explains it better.

Tyler Cowans says:

The kinetic energy didn't turn into heat by rubbing against air particles, heat is the transfer of energy. The kinetic energy transferred to internal energy, raising the temperature of the air.

aniswar lax says:

Dude you are some of the best professors out there you make mine look like a disappointment.

Melvin Davis says:

W 􏰊> 0: work done by the system W <􏰉 0: work done on the system my text book says like this i dont know its correct or the one in the viedo is correct plz help 14:04

Anupam says:

http://physicsteacher.in/2017/11/15/first-law-of-thermodynamics/

Akbaer says:

I got a dumb question, how many energy are there in the universe?

Kroschel Holmes says:

Awesome khanacdemy

lorderik237 says:

Could the first law of thermodynamics prove the idea of reincarnation? Since energy cannot be created or destroyed, and since humans have energy within them, with the "you" feeling inside your head being nothing but a 20-watt cloud of energy, wouldn't that mean that something must happen to it all after death?

shivam saini says:

is there any thing which oppose this law??? plzz tell to meee….

pixelsmart says:

Is the author's 'pendulum' analogy at 11:45 wrong? He said a vibrating molecule that momentarily comes to a stop has ho kinetic energy and only potential energy like a pendulum. I want to ask ' does the momentarily stationary molecule really have potential energy?' If the vibration is caused by a collision with another molecule then the molecule does not have potential energy while momentarily stationary. Similar to pool balls. A momentarily stationary pool ball does not have potential energy which later gets converter to kinetic energy.

Vary super cool & good topics

Kroschel Holmes says:

Whats the difference between work done and pressure volume work?

Zoha Butt says:

Amazing

Angelo Quimoyog says:

I’m confuse. Shouldn’t the kinetic energy increase from potential energy, as the ball travels downward; with the help of gravity pulling it down?

omu purkayastha says:

Some videos shw U=q+w nd sme shws q=U+W… which one is correct?? M totally confused

Anonymous alien says:

Game of thrones brought me here

Chumani Sokhetye says:

So in the case flash paper, if one burns the paper it just disappear . So what has been done to the energy not destroyed????

Sillylion says:

Wouldn't throwing the ball up meet the same amount of air resistance as it would when falling? Thus making the speed of the ball the same both ways?

Timeline says:

Who got a quiz on this lmao

Kaylia Dodge says:

wow this was so easy to understand. If only one of my teachers came close to this.

Alex Szatmary says:

Moving the ball up in air, you talking about friction with the air (what is the less important). The most IMPORTANT loss of energy of the ball is for DISPLACEMENT of air from the front of it.

I don't know what it is but i cant remember any thing about thermodynamics even though people tell me I should not be trying to learn this because I'm too young but it is quite interesting

Anthony R says:

Thermo is evil

Drake Danos says:

Where does the kinetic energy go when falling on a planet with no atmosphere?

WP Randall says:

If energy cannot be created, then it must have existed forever. But if it did, it would have to go back into the infinite beginning of time, which is not in reality. Time does not begin in a moment of time, but in infinity. What would be before it? No time, but no time doesn't continue, so time would replace no time. Only the abstract concepts, such as love, hate, math, geometry, truth, etc. exist there. If you tried to find their beginning, they would be there no matter how far you go back. Only at infinity would you find their source, but not energy; it is generated in a moment of time. Energy has to come from a created source in real time-space.

Donald Fink says:

Your example of an object moving upwards does not factor in the external force to propel the object.

Dr.derp says:

who formulated this law?

In Vino Veritas says:

WHY do we have to learn this in med school…hate my prof lmao. Ty buddy

Nic Crawford says:

What is kinetic energy measured in?

للا سف ليست هناك ترجمة للعربية

this is the coolest video i have ever seen….I love Khan Academy

Reuel Mwambali says:

This makes more sense now than when my teacher was explaining it in class

Ellie Bañez says:

What is the significance of 13.375 in physics and the universe? Any insights?

M- Nice says:

First law of thermodynamics- Never talk about thermodynamics.

Chris Manley says:

Up and 10:14

Jāmz says:

This is making alot of sense thanks you sal for your spend tim to save me from headaches at night😊

Patrick Ramirez says:

Is this the physics application or chemistry?

Iskandar Zulkarnain says:

The Martian brought me here…

Jenny Deng says:

Wait isn’t it the same as conservation of energy?

Niruni says:

Khan this is very useful ……

Abel Ubina says:

Hello Sir,

When I computed the work done in pool (billiard) the white mother ball break the 15ball. The work brought OUT is more than the work brought IN. Let’s try to compute.

F = 30lbs (White Mother Ball); D = 3ft (From the white mother ball to the first ball to strike)

SOLVE FOR ENERGY IN
W = F X D;  W = 30lbs  x  3ft  =  @t.          ENERGY IN

SOLVE FOR ENERGY OUT
First two ball extreme corner of the billiard ball 2 out of 15 ball
W = F X D; W = 30lbs x 3ft = @t  X  2ball = @t.

The remaining ball (13pcs ball) can produce more than @t.
The computation shows that the output work done is higher than the input work done
so the theory of conservation of energy is misconception.