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## Homework Statement

Show that the change in internal energy of a simple system between states (V1, T1)

and (V2, T2) is given by

[tex]∆U = \int^{T1}_{T2} C_v\ dT + \int^{V1}_{V2} T.\frac{\partial p}{\partial T}|_V - p \ dV[/tex]

## Homework Equations

dU=dQ-pdV

## The Attempt at a Solution

As U is a function of state i wrote down [tex]dU =\frac{\partial U}{\partial T}|_V dT + \frac{\partial U}{\partial V}|_T dV[/tex]

[tex]\frac{\partial U}{\partial T}|_V[/tex] is clearly just Cv but i can't get the other part into the correct form, my manipulation is just going around in circles.