The equation of state for a gas is given by $$PV = nRT + \alpha V$$, where n is the number of moles and $$\alpha$$ is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are T$$_0$$ and P$$_0$$ respectively. The work done by the gas when its temperature doubles isobarically will be:

A

$$P_0 T_0 \ln 2$$

B

$$\frac{P_0 T_0 R}{P_0 + \alpha}$$

C

$$\frac{P_0 T_0 R}{P_0 - \alpha}$$

D

$$P_0 T_0 R$$