One mole of oxygen gas is made to undergo a process in which its molar heat capacity C depends on its absolute temperature T as C = α T , where α is a positive constant. Work done by the gas when heated from an initial temperature T 0 to a final temperature 2 T 0 will be

Step-by-step solution

C = C v + W ' ⇒ W ' = d W n d T (where W ' is the work done by the gas per unit mole per unit rise in temperature) ⇒ W ' = α T - C v = α T - 5 R / 2 Δ W = ∫  W ' d T = ∫ T 0 2 T 0 α T - 5 R 2 d T = 3 α T 0 - 5 R T 0 2