The equation of state for a gas is given by PV = nRT + \(\alpha V\), where n is the number of moles and \(\alpha\) a positive constant. The initial pressure and temperature of 1 mol of the gas contained in a cylinder is Po and To, respectively. The work done by the gas when its temperature doubles isobarically will be : 

\(\frac{P_o T_o R}{P_o - \alpha}\)

\(\Delta W = P \Delta V\) ; given : \(PV = \mu RT + \alpha V\)

\(P \alpha V = \mu R \Delta T + \alpha \Delta V\)

\(\Delta V = \frac{\mu R \Delta T}{P_o} - \alpha\)

\(\Delta w = \frac{P_o R T_o}{P_o - \alpha} \text{ ... } (\mu = 1)\)