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I am wondering if equation

$$C_v=(\frac{∂U}{∂V})_T$$

applies only to ideal gases or applies generally for any other system?

The second question I have is can we use the following relation:

$$dU=nC_vdT$$

in processes that are non

I ask this because in my head this relation should apply only to

$$W=∫pdV=nC_v(T_1-T_2)$$

So I am confused whether I can use ##dU=nC_vdT## just anytime I need it (and not only for

$$C_v=(\frac{∂U}{∂V})_T$$

applies only to ideal gases or applies generally for any other system?

The second question I have is can we use the following relation:

$$dU=nC_vdT$$

in processes that are non

**isochoric**(that is for processes where volume is not constant)?I ask this because in my head this relation should apply only to

**isochoric**processes. But when calculating the work done in adiabatic process for the ideal gas I get the same result if I calculate the integral by using Poisson's relation ##PV^γ=const.## and if I use the above mentioned relation ##dU=nC_vdT##$$W=∫pdV=nC_v(T_1-T_2)$$

So I am confused whether I can use ##dU=nC_vdT## just anytime I need it (and not only for

**isochoric**process) and for any type of system (and not only for ideal gases).
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