The molar specific heat capacity of a certain gas is expressed as $$C = C_V + \alpha\frac{P}{T}$$. The equation of state for the process can be written as, where $$\alpha$$ and $$A$$ are constants.

A

$$PV = RT$$

B

$$V = \alpha T^2$$

C

$$V^2 = \alpha\ln T$$

D

$$T = A e^{V/\alpha}$$