First law of thermodynamics / internal energy | Thermodynamics | Physics | Khan Academy
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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
potential energy, and I had all kinetic energy and I had
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,
your ball made these molecules that it was bumping into vibrate
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
heat, because heat does not start with Q, but the
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
talk about heat or work you’re talking about transferring
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.

About James Carlton

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15 thoughts on “First law of thermodynamics / internal energy | Thermodynamics | Physics | Khan Academy

  1. 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)

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

    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.
    Appreciated for your reply

    Thank you.

    Abel Urbina

  2. Man I'm first year chemistry and our stuff is WAY more complicated than this. we have pages upon pages of demonstrations and equations and integrals/derivatives and all that. any online classes that go into more details ??

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