First Law of Thermodynamics: Energy, Internal Energy, Equation

Name: First law of thermodynamics / internal energy | Thermodynamics | Physics | Khan Academy
Uploaded: 2009-09-16T18:07:23+00:00
Duration: 17 min 40 s
Channel: Khan Academy
Description: Summary and key takeaways on First Law of Thermodynamics: Energy, Internal Energy, Equation, covering The First Law of Thermodynamics Energy cannot be created

Khan Academy

Sep 16, 2009

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17 min video

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YouTube video ID: Xb05CaG7TsQ

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Energy cannot be created or destroyed; it can only be transformed from one form to another. In projectile motion, the ball’s kinetic energy converts to potential energy as it rises, then back to kinetic energy on the way down. When air resistance acts, the ball’s kinetic energy is transferred to air molecules through friction, raising their kinetic energy and manifesting as heat. Temperature therefore represents the average kinetic energy of the molecules in a macrostate.

Internal Energy (U)

Internal energy, denoted U, is the total energy contained within a system. It aggregates translational and rotational kinetic energy, vibrational and bond potential energy, and electrical potential energy of all particles. For a mono‑atomic ideal gas, internal energy simplifies to the kinetic energy of the gas particles alone, making U a macrostate description of the system.

The First Law Equation

The change in internal energy (ΔU) equals the heat added to the system (Q) plus the work done on the system (W), or alternatively ΔU = Q – W when work is defined as done by the system. Adding heat raises U, while doing work transfers energy away, lowering U. These sign conventions ensure the equation reflects the reality that energy transferred as work leaves the system, whereas heat input adds energy.

Mechanisms in Action

Energy transformation in a projectile: kinetic → potential at the peak → kinetic on descent.
Friction and heat transfer: moving objects lose kinetic energy to surrounding air molecules via collisions, increasing molecular vibration and temperature.
Internal energy calculation: sum all microscopic energy forms—translational, rotational, vibrational, bond, and electrical—within the defined system.

Takeaways

Energy cannot be created or destroyed; it only changes form, as shown by kinetic energy converting to potential energy in a projectile.
Air resistance transfers kinetic energy to surrounding molecules, increasing their kinetic energy and appearing as heat that raises temperature.
Internal energy (U) is the total microscopic energy of a system, encompassing kinetic, vibrational, bond, and electrical potential components.
For a monoatomic ideal gas, internal energy reduces to the kinetic energy of the gas particles, simplifying the description of U.
The First Law equation ΔU = Q – W (or ΔU = Q + W) links internal energy changes to heat added and work done, reflecting that work removes energy while heat adds it.

Frequently Asked Questions

Why does kinetic energy become heat when air resistance is present?

Kinetic energy becomes heat because friction with air molecules transfers the object's motion energy to the molecules, increasing their random kinetic motion. This rise in molecular motion is measured as a temperature increase, which we identify as heat.

What is the difference between the two sign conventions for work in the First Law equation?

One convention defines work done by the system as positive, giving ΔU = Q – W; the other defines work done on the system as positive, giving ΔU = Q + W. Both express the same energy balance, differing only in the sign assigned to work.

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– W when work is defined as done by the system. Adding heat raises U, while doing work transfers energy away, lowering U. These sign conventions ensure the equation reflects the reality that energy transferred as work leaves the system, whereas heat input adds energy. ## Mechanisms in Action - **Energy transformation in

projectile: kinetic → potential at the peak → kinetic on descent. - Friction and heat transfer: moving objects lose kinetic energy to surrounding air molecules via collisions, increasing molecular vibration and temperature. - Internal energy calculation:** sum all microscopic energy forms—translational, rotational, vibrational, bond, and electrical—within the defined system.

Helpful resources related to this video

If you want to practice or explore the concepts discussed in the video, these commonly used tools may help.

Physics Thermodynamics Textbook For College Students Recommended

Provides comprehensive coverage of the First Law of Thermodynamics, internal energy, and heat transfer mechanisms to reinforce the lecture concepts.

Amazon →

Demonstration Kinetic And Potential Energy Kit

Allows for hands-on observation of energy transformation between kinetic and potential states, as discussed in the projectile motion example.

Amazon →

Digital Infrared Thermometer For Heat Measurement

Enables the user to measure temperature changes caused by friction or heat transfer, illustrating the relationship between molecular kinetic energy and heat.

Amazon →

Thermodynamics And Heat Transfer Reference Book

Serves as a technical resource for the mathematical representations of internal energy and work-heat sign conventions.

Amazon →

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Full Transcript YouTube

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.

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Internal Energy (U)

The First Law Equation

Mechanisms in Action

Takeaways

Frequently Asked Questions

Why does kinetic energy become heat when air resistance is present?

What is the difference between the two sign conventions for work in the First Law equation?

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