In the last video we defined

internal energy as literally all the energy that’s

in a system. That’s kind of the most

inclusive version, at least in my head. So that’s my system, it’s

some type of container. And I have a bunch of

particles in here. It’s literally the sum of

the kinetic energies of all these particles. If they had potential

energies, we’d throw that in there. If they have electrical

potential, we’d throw that in there. If they have bonds with each

other, the energies in that bond, we would throw

it in there. It’s everything. It’s all inclusive. And, I told you in the last

video it’s unintuitive that U stands for internal energy. But I kind of think that, you

know, U, it contains the universe of energy. You know, that’s just for

me to memorize it. Don’t think too deeply into

what I just said. But this is internal energy. If you show me a system, it

has some internal energy. It’s a function of its state. I don’t care how it got to that

state, but if you told me a system at a certain state,

maybe with a certain pressure, or a certain volume, or at a

certain temperature– although if you give me pressure and

volume that should be enough– I can tell you what its

internal energy is. Especially if you tell me the

type of molecule I have, and things like that. Now we also said in the last

video that because internal energy is all the energy in

the system, it can’t be randomly created or destroyed. It can just be transformed

from one form to another. So if I have a change in

internal energy, it can only be due to– well, it can be

due to more than what I’m describing. But in our simple world where

all of the energy in a system– and maybe we’re dealing

with gases, because that’s normally what you deal

with in a first-year chemistry course– it’s going to be the

heat that could be added to the system, plus the work

done on the system. And like I said in the last

video, sometimes they’ll say, instead of plus the work done

on the system, sometimes they’ll say, minus the work

that the system does. Either way. And here I just want to make

another side discussion here, because I decided to write

it without the little deltas here. And the reason why I did that

is if you were to write this equation, which you will see,

you’ll see it in textbooks, teachers will do it– nothing

inherently criminal about that– but I just do that

because it clears in my mind what heat and what work are

relative to internal energy. If I were to write delta U is

equal to heat delta Q plus delta W to me this implies that

at some point I had some amount of heat in my system,

and then I have a different amount of heat in my system,

and I took the difference between the two and I got

a change in heat. So this implies that heat is

somehow an inherent macrostate of the system, and that’s

not the case. I can tell you what the

internal energy of this system is. I can tell you its pressure. I can tell you its volume. I can tell you its

temperature. These are all macrostates

of the system. I don’t know how it got to this

situation, but I can tell you about it. I cannot tell you what the

heat is of this system. And that might be a little

unintuitive, because if I ask you, hey I have a cup of coffee,

what’s the heat of it? You might say, oh, it’s, you

know, you might give me the temperature. Because in our everyday language

we use things like heat and temperature

interchangeably. But in thermodynamics, heat

is a transfer of energy. A way to think about it

is, if internal energy is your bank account. So you could say change

in bank account. And it really is like

the energy bank account of a system. If you have a change in a bank

account, you had some deposits or withdrawals. And heat and work are really

just deposits or withdrawals into our energy bank account. Heat is one kind. Maybe heat is like

a wire transfer. So you could say it’s wire

transfers to your account. Transfers to your account

plus check deposits. Now it makes a lot of sense to

say, you could say, what is my value of my bank account? Or you could say what is my

change in my bank account? You take two snapshots of

your bank account at two different times. But would it make sense to say–

you know, I could say I wire transferred $10, right? So I could say, this statement

would be plus $10. And I could say that I

wrote $20 in checks, minus $20 in checks. In which case, my change

in my bank account would be minus $10. Now would it make sense

for me to say change in wire transfer? That implies that when I started

off maybe my bank account had $100 in it

and now it has $90. When my bank account had $100

in it, did it have any wire transfer amount? No, wire transfer was how money

was deposited or taken away from my account. Likewise, it didn’t have a

checking deposit account, so I can’t really– it just seems

weird to me to say change in wire transfer is $10, or change

in check deposits is $20 or minus $20. Would you say, I made a

$10 wire transfer and I paid $20 in checks. So I had a net change in

my bank account of $10. Likewise, I say how much work

was done to me or I did, which is essentially a deposit or

withdrawal of energy. Or I could say much heat was

given to me or how much heat was released, which is another

way of depositing or withdrawing energy from my

energy bank account. So that’s why I like

to stick to this. And I like to stay

away from this. And just like I said, you can’t

say how much heat is in the system. So someone will say, oh, how

much heat is in this? You cannot say that. There’s no heat state variable

for that system. You have internal energy. The closest thing to heat,

we’ll talk about it in a future video, is enthalpy. Enthalpy is essentially a way of

measuring how much heat is in a system, but we won’t talk

about that just now. And you can’t say how much

work is in a system. You can’t say, oh I have x

amount of work in a system. The system can do work or have

work done to it, but there’s not a certain amount of work,

because that energy in the system could be all used for

work, it could all be used for heat, it could all be used for

a ton of different things. So you can’t say those things. And that’s why I don’t like

treating them like state variables, or state functions. So with that said, this

is our definition. Let’s do a couple of

simple problems, just to give you intuition. And I really want to make

you comfortable. My real goal is to make you

comfortable with, when to know to use plus or minus

on the work. And the best way to do it is not

to memorize a formula, but just to kind of think about

what’s happening. So let’s say that I have some

system here and, I don’t know, it’s a balloon. And let’s say that I have no

change in internal energy. Internal energy is 0. And for our purposes we can kind

of view it as the kinetic energy of the particles

haven’t changed. And let’s say by expanding a

bit, by my balloon expanding a bit– I did some work. I’ll do this in more detail

in the next video. So the system does 10

joules of work. My question is, how much heat

was added or taken away from the system? So the way I can think about

it– you don’t even have to write the formula down, or you

can write it– you could say, look, the internal energy, the

amount of energy in the system hasn’t changed. The system did 10

joules of work. So that’s energy going

out of the system. It did 10 joules. So 10 joules went out

in the form of work. If the internal energy did not

change, then essentially 10 joules of energy had to

go into the system. 10 joules had to go

into the system. If it didn’t, the internal

energy would have gone down by the amount of work we had. And the only way, if is this is

the net work, the only way that we’re talking about, that

we can add energy outside of work, is through heat. So 10 joules of heat must

have been added. So we can write 10 joules

of heat added to system. Now let’s look at that from

the point of view of the actual formula. If we have delta U is equal to

heat added, plus work done to the system, then we would

say, OK, this was 0. It’s equal to the heat

added to the system. Remember, in this way we’re

saying this is the heat done, or the work done,

to the system. W is work done. Now, the system did work

to something else. It didn’t have work

done to it. So if this is work done to the

system, and it did work, then this is going to

be a minus 10. Minus 10 joules. And then you solve both

sides of this. You add 10 to both sides and

you get 10 is equal to Q, which is exactly what

we got up here. But this can get confusing

sometimes, because you’re like, oh, is this heat

that the system did? Is this heat that was added to

the system or taken away? The convention tends to be

that this is heat added. But then sometimes

it’s confusing. Is this the work done to the

system or work done by? And that’s why I like just

doing it this way. If the system does work

it loses energy. If the system has work done

to it, it gains energy. So let’s do another problem. I mean, I could have done this

exact same thing using the other formula that you’ll

sometimes see. Delta U is equal to Q minus the

work that the system does by the system– Work

done by the system. And in this case, once

again, change in internal energy was 0. That is equal to heat

added to the system, minus the work done. So minus– I told you at the

beginning of the problem that the system did 10 joules of

work– so minus the work done. Minus 10 joules. We get the same situation

up here from two different formulas. And we got 10 is equal to Q. Either way, the heat added to

the system is 10 joules. Let’s do one more. Let’s say that, I don’t know,

5 joules of heat taken away from system. And let’s say that 1 joule

of work done on system. So maybe we’re compressing the

balloon on the system. What is our change in

internal energy? Let’s just figure

out our change. So the way I think of it is 5

joules of heat taken away from the system, that’s going

to reduce our internal energy by minus 5. And if 1 joule work is done onto

the system, we’re putting energy into it so that’ll

be plus 1. So minus 5, plus 1, is

going to be minus 4. Or enter our change in internal energy is minus 4 joules. Now we could have done that a

little bit more formally with the formula, change in internal

energy is equal to heat added to the system, plus

work done on the system. So it’s equal to heat

added to the system. We had 5 joules heat taken away,

so this is minus 5, plus work done on the system. We have 1 joule of work done

on the system, and there we get, once again, minus 4. Now, I could have written that

same formula the other way. I could have said change in

internal energy is equal to heat added to the system minus

the work that the system does. I want to do this both ways,

because I don’t want you to get confused, either way you

see it on problems or in school, or maybe you take one

class that does it one way and one class that does

it the other. If you use it this way,

what was the heat added to the system? We had heat taken away,

so it’s minus 5. So minus the work that the

system does, how much work does the system do? Well, the system had 1 joule

of work done to it. So it did itself minus

1 joules of work. So it’s minus minus 1. I want to be clear, when I use

this formula, this is work done by system, done by. This is work done to. The system had work

done to it. So it had minus 1 joules of work

done by the system, so these become pluses, and you

get back to a minus 4. Do whatever’s intuitive

for you. For me, this tends to be the

most intuitive, where you don’t even use a formula. We just think, if I’m doing

work, I’m using up energy. If I get work done to me, I’m

being handed over energy. If I have heat taken away from

me, I’m giving away energy. If I have heat added to me,

I’m getting energy. See you in the next video.