Derive the expression for isothermal change in Constant Volume Heat Capacity

[eagerbeaver92]

Homework Statement

Derive the following expression for calculating the isothermal change in Constant Volume Heat Capacity:

(dC_v/dV)_T = T(d²P/dT²)_V

Homework Equations

The Attempt at a Solution

I have no idea, please help

 

[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