How can heat capacity be determined when both pressure and volume are changing?

[gsyz]

Hello all,

I am taking a thermodynamics course and unfortunately my professor is not very instructive. I have attended every class and I still feel lost.

I was wondering how it is possible to find heat capacity if both the pressure and the volume are changing? I was under the impression that one or the other had to be held constant.

Also, what is a polytropic process? He uses the term in homeworks but it never appears in the textbook.

Any help would be greatly appreciated, I'm feeling very frustrated by the lack of understanding the material.

Thanks, gsyz

 

[jack action]

I was wondering how it is possible to find heat capacity if both the pressure and the volume are changing?

Heat capacity is the ratio of the heat added to an object to the resulting temperature change.

This is straight forward for a solid. For a gas, there is also a volume change when the gas is heated and this implies work was done on the gas. Obviously, the energy came for the heat, so one could say that it did not contribute to the temperature change. But then, nothing in the initial definition states that there most not be a volume change. The full characteristics of a gas can be known from 2 values of heat capacity, one measured at constant volume and one measured at constant pressure.

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Also, what is a polytropic process?

A polytropic process is a generic process that obeys the relation $pv^n =C$.

The fun thing about this process is that you can model all common thermodynamic processes:

if $n = 0$, it's an isobaric process;
if $n = +\infty$, it's an isochoric process;
if $n = 1$, it's an isothermic process;
if $n = \gamma$, it's an adiabatic process.

So you can measure pressure and volume of a gas undergoing a certain process and by analyzing the exponent that best fit your data, you can tell which process was actually happening.

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