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
  $\frac{P_0 T_0 R}{P_0 - \alpha}$
• B
  $\frac{P_0 T_0 R}{P_0 + \alpha}$
• C
  $P_0 T_0 R \ln 2$
• D
  $P_0 T_0 R$