Consider the following total differential of the internal energy U of one more of a berthelot gas with heat capacity Cv ( not necessary to be a constant) and interaction strength a(>0). dU = CvdT + a/ TV^2 dV. Based on the given differential answer the following questions.

A. Derive the appropriate expression of the internal pressure piT for the berthelot gas.

Should the internal pressure piT of the berthelot gas be greater than equal to or less than zero? Explain your choice(s)

C. Derive an expression of (dt/dv)u for the berthelot gas.

D. Derive the appropriate expression of (dCv/dv)T for the berthelot gas

Note the differential the wright differential symbols is shown on the attached picture