The molar specific heat of an ideal gas in a certain thermodynamic process is $$\frac{\alpha}{T}$$ where $$\alpha$$ is a constant. If the adiabatic exponent is $$\gamma = \frac{C_P}{C_V}$$, the work done in heating one mole of the gas from $$T_0$$ to $$nT_0$$ is

A

$$\frac{1}{\alpha}\ln n$$

B

$$\alpha \ln n - \frac{(n - 1)}{(\gamma - 1)} RT_0 $$

C

$$\alpha \ln n - (\gamma - 1) RT_0$$

D

$$\frac{(n - 1)}{(\gamma - 1)}RT_0$$