Heat capacities, adiabatic processes, etc

[member 392791]

I am confused why the heat capacity at constant pressure can be different from the heat capacity at constant volume.

I am also having difficulties absorbing the material regarding the kinetic theory of gases, such as keeping all the ΔE_int changes with what processes etc.

Why can adiabatic processes be treated as isovolumetric when going from one isotherm to another?? How is work calculated?

I know I just brought up a lot of different concepts here, but I am very lost when reading about it in my book.

 

[russ_watters]

I am confused why the heat capacity at constant pressure can be different from the heat capacity at constant volume.

Pressure holds energy too, so if you are holding the volume constant and the pressure increases, you raise the temperature and the pressure instead of just the temperature. So a portion of the heat added doesn't result in a higher temperature -- thus C_v is lower.

Why can adiabatic processes be treated as isovolumetric when going from one isotherm to another?? How is work calculated?

That one, the wording isn't clicking for me -- do you have a reference?

 

[member 392791]

From my textbook

''All three variables in the ideal gas law—P, V, and T—change
during an adiabatic process.
Let’s imagine an adiabatic gas process involving an infinitesimal change in
volume dV and an accompanying infinitesimal change in temperature dT. The
work done on the gas is -P dV.''

If P changes during an adiabatic process, you can only use -p dV if you know P as a function of V, right?

Then for what I was saying

''Because the internal energy of an ideal gas depends
only on temperature, the change in the internal energy in an adiabatic process
is the same as that for an isovolumetric process between the same temperatures,''