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

Summary

This educational video script delves into the first law of thermodynamics, highlighting the principle that energy cannot be created or destroyed but only transformed. The presenter uses the example of a ball thrown into the air to illustrate the conversion of kinetic energy to potential energy and back, and how air resistance results in a loss of kinetic energy due to heat transfer. The concept of internal energy as a macroscopic description of all energy within a system is introduced, with a focus on its components like kinetic and potential energy. The script concludes with a discussion on how changes in internal energy relate to heat transfer and work done, setting the stage for further exploration in upcoming videos.

Takeaways

• 🔄 The first law of thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another.
• 🏋️‍♂️ Kinetic energy is the energy of movement, and as an object slows down, its kinetic energy decreases.
• 📈 Potential energy is the stored energy an object possesses due to its position or condition, which can be converted into other forms of energy.
• 🪁 When a ball is thrown upwards, its kinetic energy is converted into potential energy at its peak, and then back into kinetic energy as it falls.
• 💨 Air resistance can reduce the kinetic energy of a falling object, converting some of it into heat through friction with air molecules.
• 🌡️ Temperature is a measure of the average kinetic energy of the particles in a substance, reflecting their movement.
• 🔄 Internal energy (U) encompasses all the energy contained within a system, including kinetic and potential energies of particles.
• 🔧 The change in internal energy (∆U) can be calculated as the heat added to the system (Q) minus the work done by the system (W), or as Q plus the work done on the system, depending on the perspective.
• ⚖️ In thermodynamics, work and heat transfer are ways of energy exchange between a system and its surroundings, affecting the system's internal energy.
• 📚 The video script promises further exploration of these concepts, including practical examples and different notations used in thermodynamics.

Q & A

What is the first law of thermodynamics?

The first law of thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another.

How does the concept of kinetic energy relate to the first law of thermodynamics?

Kinetic energy is a form of energy that is associated with the motion of an object. According to the first law of thermodynamics, when an object's kinetic energy decreases, it does not disappear but is transformed into another form of energy, such as potential energy.

What is potential energy and how does it connect to the first law?

Potential energy is the stored energy of an object due to its position or condition. It can be converted into other forms of energy, like kinetic energy. The first law of thermodynamics ensures that this conversion does not create or destroy energy but merely transforms it from one form to another.

Can you explain the example of throwing a ball up in the air in terms of energy transformation?

When a ball is thrown up, its kinetic energy is converted to potential energy as it rises and comes to a stop at its peak. On the way down, potential energy is converted back to kinetic energy. If air resistance is considered, some of the kinetic energy is transformed into heat due to friction with air molecules.

What happens to the energy when air resistance is present during the ball's motion?

In the presence of air resistance, some of the ball's kinetic energy is converted into heat as the ball rubs against air molecules, causing them to vibrate faster. This results in the ball having less kinetic energy when it returns to the starting point compared to when it was initially thrown.

What is internal energy and how is it measured?

Internal energy is the total energy contained within a system, which includes kinetic and potential energies of molecules, energy from molecular bonds, and other forms of energy present. It is typically measured as the change in internal energy (ΔU), which can be calculated from the heat added to the system (Q) and the work done by the system (W).

How does the first law of thermodynamics relate to the concept of internal energy?

The first law of thermodynamics implies that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. This relationship shows that energy is conserved, with internal energy changes resulting from transfers of energy in the form of heat and work.

What is the significance of the equation ΔU = Q - W in thermodynamics?

The equation ΔU = Q - W is a mathematical representation of the first law of thermodynamics. It shows that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W), illustrating the conservation of energy principle.

Why is it important to understand the difference between heat (Q) and work (W) in thermodynamics?

Understanding the difference between heat and work is crucial because they represent different modes of energy transfer. Heat is the transfer of energy due to a temperature difference, while work is the transfer of energy by a force moving an object. Recognizing these differences helps in accurately applying the first law of thermodynamics to various systems.

Can you provide an example of how internal energy can change in a system?

An example of internal energy changing in a system is when a gas is heated. As the gas absorbs heat (Q is positive), its internal energy increases (ΔU is positive). If the gas expands and does work on its surroundings (W is positive), the increase in internal energy will be the sum of the heat added and the work done by the gas.

Outlines

00:00

🔄 The First Law of Thermodynamics

This paragraph introduces the first law of thermodynamics, which states that energy cannot be created or destroyed, only transformed. The speaker uses the example of throwing a ball straight up to illustrate the transformation of kinetic energy into potential energy and back into kinetic energy. The concept is further explored by considering the effect of air resistance, which reduces the ball's velocity upon return, indicating that some of the kinetic energy has been transformed into heat due to friction with air molecules.

05:00

🌡️ Energy Transformation and Internal Energy

The speaker delves into the concept of energy transformation, particularly focusing on the example where air resistance causes a ball's kinetic energy to be partially converted into heat, raising the temperature of the air molecules it interacts with. The paragraph transitions into a discussion of internal energy, which is a macroscopic description of all the energy contained within a system, including kinetic and potential energies of molecules, as well as energy associated with molecular bonds and electron configurations.

10:04

🔧 Internal Energy and Its Components

The paragraph discusses the components of internal energy in more detail, focusing on the example of a metal. It explains that internal energy encompasses not only the kinetic energy of moving particles but also potential energy associated with particle vibrations and electron configurations. The speaker clarifies that for an ideal gas, and especially for a monoatomic ideal gas, internal energy can be simplified to just the kinetic energy of the particles, excluding other complexities.

15:06

⚖️ The First Law of Thermodynamics and Energy Transfer

In the final paragraph, the speaker connects the first law of thermodynamics to the concept of energy transfer, specifically in terms of heat and work. The relationship between changes in internal energy (ΔU) and the system's interactions with its surroundings (heat added and work done) is explored. The speaker emphasizes the importance of understanding the signs associated with heat and work in these equations, noting that heat added to a system or work done on a system results in an increase in internal energy, while heat lost or work done by the system results in a decrease.

Keywords

💡Thermodynamics

Thermodynamics is the study of the movement of heat and the conversion of different forms of energy. In the video, thermodynamics is central to understanding how energy is neither created nor destroyed but transformed, which is a fundamental principle of the first law of thermodynamics.

💡First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. The video uses this law to explain the transformation of kinetic energy into potential energy and vice versa, as well as the concept of energy conservation.

💡Kinetic Energy

Kinetic energy is the energy of motion. The video illustrates this concept by discussing the example of a ball thrown into the air, which has kinetic energy when it is moving and none when it is momentarily stationary at its peak.

💡Potential Energy

Potential energy is the stored energy of an object due to its position or condition. In the video, potential energy is discussed in the context of the ball thrown into the air, which gains potential energy as it rises and loses it as it falls.

💡Internal Energy

Internal energy refers to the total energy contained within a system. It includes all forms of energy such as kinetic and potential energy of molecules. The video explains that internal energy is a macroscopic description of all the microscopic forms of energy within a system.

💡Heat

Heat is a form of energy transfer due to temperature difference. The video discusses how heat is a result of the transfer of kinetic energy from a moving object, like the ball, to the air molecules it encounters, which increases their kinetic energy and thus temperature.

💡Friction

Friction is the force that opposes the relative motion or tendency of such motion of two surfaces in contact. In the video, friction is mentioned as the cause of energy loss due to air resistance, which converts some of the ball's kinetic energy into heat.

💡Air Resistance

Air resistance is the force that opposes the motion of an object through the air. The video uses air resistance to explain how it reduces the kinetic energy of the falling ball, which is then transformed into heat.

💡Work

Work is a measure of energy transfer that occurs when an object is moved by an external force. The video discusses work in the context of energy transfer, where doing work on a system increases its internal energy, and work done by the system decreases it.

💡Ideal Gas

An ideal gas is a theoretical gas that follows the ideal gas law, PV=nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. The video simplifies the discussion of internal energy by assuming the system is an ideal gas, which does not have intermolecular forces or potential energy.

💡Monoatomic Ideal Gas

A monoatomic ideal gas is a type of ideal gas composed of individual atoms that do not have significant intermolecular forces. The video suggests considering monoatomic ideal gases like helium or neon for simplicity in understanding internal energy as primarily kinetic energy.

Highlights

Introduction to the first law of thermodynamics, which states that energy cannot be created or destroyed, only transformed.

Explanation of energy transformation using the example of throwing a ball straight up, illustrating the conversion between kinetic and potential energy.

Discussion on the effect of air resistance on energy transformation, showing how kinetic energy is reduced due to friction with air molecules.

Clarification that lost kinetic energy due to air resistance is transferred to air molecules, increasing their kinetic energy and thus the temperature of the air.

Introduction to the concept of internal energy, which is the total energy contained within a system.

Description of internal energy components, including kinetic and potential energy of molecules, as well as energy from molecular bonds.

Simplification of internal energy for monoatomic ideal gases, where it can be considered as purely kinetic energy of the atoms.

Explanation of how the first law of thermodynamics applies to changes in internal energy, relating it to heat transfer and work done.

Different ways to express the first law of thermodynamics in terms of internal energy, heat, and work, emphasizing the importance of understanding the direction of energy transfer.

The significance of the direction of work done in relation to the change in internal energy, where work done by the system results in a loss of internal energy.

The impact of heat transfer on internal energy, where heat added to a system increases its internal energy.

The potential confusion between the terms 'change in heat' and 'heat added', and the importance of understanding the context in which they are used.

The relationship between work done and energy transfer, where work done by the system results in a decrease in internal energy, and work done on the system results in an increase.

A preview of upcoming examples that will further illustrate the concept of internal energy, heat, and work in the context of the first law of thermodynamics.

Transcripts

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.