Question

The temperature of $ n $ moles of an ideal gas is increased from $ T $ to $ 4T $ through a process for which pressure $ P = aT^{-1} $ where a is a constant. Then, the work done by the gas is

• A. $ nRT $
• B. $ 4 nRT $
• C. $ 2 nRT $
• D. $ 6 nRT $

Answer 1

Answer: (D)

According to an ideal gas equation
$ PV = nRT $ or $ V= \frac{nRT}{P} $
$ \because P = \frac{a}{T} $ (given) $ \quad...(i) $
$ \therefore V = \frac {nRT^{2}}{a} $
$ \Rightarrow dV = \frac{2nRT}{a} dT \quad ...(ii) $
Work done by the gas, $ dW = PdV $
or $ W = \int\limits_{T}^{4T} \frac{a}{T} \frac{2nRT }{a}dT \quad $ (Using $ (i) $ and $ (ii) $ )
$ = [2n RT]_{T}^{4T} = 6nRT $