The internal energy of a gas obeying P (V - b) RT (where, b is a positive constant and has a constant C_v), depends upon its

Solution(By Examveda Team)

The internal energy of an gas is given by:
$$\eqalign{ & dU = CvdT - \left[ {P + T\left( {\frac{{\left( {\frac{{\partial V}}{{\partial T}}} \right)p}}{{\left( {\frac{{\partial V}}{{\partial P}}} \right)T}}} \right)dV} \right] \cr & \Rightarrow dU = CvdT + \left[ {T\left( {\frac{{\partial p}}{{\partial {T_V}}}} \right) - p} \right] \cr & {\text{using the given equation:}} \cr & P\left( {v - b} \right) = RT \cr & \Rightarrow \frac{{\partial P}}{{\partial T}} = \frac{R}{V} \cr & \Rightarrow dU = {c_v}dT \cr} $$
Hence internal energy is only a function of temperature.