Thermo Final Review - specific heat for ideal gas

[dwsky]

TL;DR Summary: why is the answer "all of the above"?

Could someone explain why the correct answer is all of the above? I understand that Cv implies a constant volume process, but what about the other two?

 

[Hill]

Because internal energy of an ideal gas depends only on its temperature.

 

[TSny]

I understand that Cv implies a constant volume process, but what about the other two?

The fact that you can write the internal energy of an ideal gas as $U = C_{_V} T$ doesn't mean that this formula can only be used in constant-volume processes. Internal energy is a state variable and for an ideal gas $U$ is proportional to the absolute temperature. In the formula $U = C_{_V} T$, think of $C_{_V}$ as just a number (with units) that gives the proportionality constant between $U$ and $T$.

Note that in the formula $U = C_{_V} T$, $C_{_V}$ is not the specific heat capacity. It's the total heat capacity which takes into account the amount of gas. Often, you see the formula written as $U = nC_{_V} T$ where $n$ is the number of moles and $C_{_V}$ now represents the molar specific heat capacity.