An ideal gas has molar heat capacity $C_V$ at constant volume. The gas undergoes a process where the temperature changes as $T=T_0(1+\alpha V^2)$, where $T$ and $V$ are temperature and volume respectively, and $T_0$ and $\alpha$ are positive constants. The molar heat capacity $C$ of the gas is given as $C=C_V+R f(V)$, where $f(V)$ is a function of volume. The expression for $f(V)$ is

• A
  $\frac{\alpha V^2}{1+\alpha V^2}$
• B
  $\frac{1+\alpha V^2}{2 \alpha V^2}$
• C
  $\alpha V^2(1+\alpha V^2)$
• D
  $\frac{1}{2 \alpha V^2(1+\alpha V^2)}$