# Doing work against the friction force, temperature, and heat

In Feynman's his introduction to the second law of thermodynamics, he said,

We know that if we do work against friction, say, the work lost to us is equal to the heat produced. If we do work in a room at temperature $$T$$, and we do the work slowly enough, the room temperature does not change much, and we have converted work into heat at a given temperature.

I suppose that if the temperature doesn't change, then the work done must go into the potential energy part of the internal energy of the gas in the room, but then why must we do the work slowly?

The last statement is also quite confusing. As I understand, work and heat are essentially the same thing: a mechanism of transferring energy from one system to another. So is it just an abuse of language when he says, "we have converted work into heat"?

• Work and heat are drastically different. Does the text not discuss the difference? Jan 1, 2020 at 20:24
• The process is carried out slowly in order to minimize energy loss. You may want to read about reversible thermodynamic processes. en.wikipedia.org/wiki/Reversible_process_(thermodynamics)
– Sam
Jan 1, 2020 at 20:26
• @AaronStevens Not really. Jan 1, 2020 at 20:29
• @Sam By energy loss, do you mean conversion into thermal energy (i.e. increasing the temperature of the room)? Jan 1, 2020 at 20:30
• Yes, in fact if you do this infinitesimally slowly over infinite time, all the energy will be converted into work and no heat will be produced.
– Sam
Jan 1, 2020 at 20:33

Feynman wants to talk about constant temperature, because that simplifies the physics: "we have converted work into heat at a given temperature"

If friction transfers a lot of energy quickly, the material where friction is acting rises in temperature: Those parts get hot, and it's no longer a constant-T situation.

So you have to have the friction act slowly, giving time for the energy lost to friction to spread out into the room and eventually into the environment of the room. Since those are quite large, their temperature doesn't change significantly when the energy is added across all of that material.

As to work and heat being the same: No, they're not. That's the point. Later, in the book, you'll see more about that.

His "converted work into heat at a given temperature" is saying that work, the mechanical transfer of energy, has been changed into heat, the thermal transfer of energy. (Later you'll learn that, while it can go this way, going the other way is more complicated)

If you find yourself thinking that Feynman is committing an "abuse of language", that's a good clue that you're acting on an incorrect assumption or a misunderstanding. His knowledge of physics and how to explain it were both above average.

• Feyman's knowledge of physics and how to explain it were both above average. but this does not imply that he was always perfect in his wording. He was a man of his time and sometimes he used a language which is now recognised not to be the optimal for avoiding misunderstanding and misconceptions. This is one of those cases. In the cited sntence, feynman is using the word heat to mean internal energy. It is even more clear a few lines after the cited sentencs. He said "...one could not convert any of its heat energy into work.." He was clearly using heat and heat energy in place ...(continue) Jan 1, 2020 at 22:20
• @Bob Jacobsen I should've said similar, instead of same. Both heat and work are means of transferring energy. I noticed that he often spoke of heat as if it were a property of an object; for instance, he said,"we might think that heat energy, such as that in the vibrational motions of molecules, might provide a goodly supply of useful energy." And if we interpret heat as being a property/energy of an object, then "converting work into heat" certainly makes more sense, I think. Jan 1, 2020 at 22:20
• @GiorgioP Exactly, considering heat as form of internal energy clarifies everything now. Jan 1, 2020 at 22:22
• ... of internal energy. Nowadays, Physics Education Research has recognized the importance of using words which could minimize confusion between heat and internal energy. Feynman cannot be blamed for having given his lectures much before, still it is important to notice that thre has been some evolution in teaching. Jan 1, 2020 at 22:25
• "heat" is not the same thing as "heat energy"; different language for different things. Here @GiorgioP's point is correct: "heat energy" can be a confusing term, which tempts you to truncate to "heat"; that would be an error. "Thermal energy" is better, because "thermal" isn't a word we use by itself. (And the point is that "heat energy" is a form of energy that you can't tap into, isn't it?) Jan 1, 2020 at 23:50