Question

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 $T_o$ at a final temperature $2T_o$, will be

• A. $4\alpha {T_o}^2$
• B. $(\alpha T_o-R)\frac{3T_o}{2}$
• C. $(3\alpha T_o-5R)\frac{T_o}{2}$
• D. none of these

Answer 1

Answer: (C)

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

$W=dQ-dU$

$={}_{T_0}^{2T_0}\int CdT-\frac{f}{2}R(2T_0-T_0)$

$=\frac{3}{2}\alpha T_0^2-\frac{5}{2}R{T}_0$

$=(3\alpha T_0-5R)\frac{T_0}{2}$