oxygen gas is made to undergo a process in which its molar heat capacity C depends on its absolute temperature T as c = \(\alpha T\). Work done by it when heated from an initial temperature T_o to a final temperature 2T_o, will be : 

\(3\alpha T_o - 5R) \frac{T_o}{2}\)

C = C_v + W'

where W' is the work done by the gas per unit mole per unit rise in temperature. So :

W' = \(\alpha T - C_v = \alpha T - \frac{5R}{2}\)

\(\Delta W = \int W' dT = \int_{T_o}^{2T_o} (\alpha T - \frac{5R}{2}) dT\)

\(\Delta W = (3 \alpha T_o - 5R)\frac{T_o}{2}\)