Derive the expression for isothermal change in Constant Volume Heat Capacity

eagerbeaver92

1. The problem statement, all variables and given/known data
Derive the following expression for calculating the isothermal change in Constant Volume Heat Capacity:

(dC_v/dV)_T = T(d²P/dT²)_V


2. Relevant equations



3. The attempt at a solution

I have no idea, please help
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

eagerbeaver92

How about this?????

assuming ideal gas:

P=nrt/V

then

(dP/dT) = R/V , ignoring moles

and

(d₂P/d²T) = 0

so (dC^v/dV)=T*0=0