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 To to a final temperature 2To, will be :
Answer & explanation
Correct answer: option 3
C = Cv + W'
where W' is the work done by the gas per unit mole per unit rise in temperature. So :
W' = \(\alpha T - C_v = \alpha T - \frac{5R}{2}\)
\(\Delta W = \int W' dT = \int_{T_o}^{2T_o} (\alpha T - \frac{5R}{2}) dT\)
\(\Delta W = (3 \alpha T_o - 5R)\frac{T_o}{2}\)