Q 11-11-137JEE MainJEE Main 2020 (7 Jan, Shift 1)Medium
A litre of dry air at STP expands adiabatically to a volume of $3$ litres. If $\gamma = 1.40$, the work done by air is: ($3^{1.4} = 4.6555$) [Take air to be an ideal gas]
Answer: (B) $90.5$ J
$P_1V_1 = 1.013\times10^5\times10^{-3} = 101.3$ J.
Adiabatic: $P_2 = P_1\left(\dfrac{V_1}{V_2}\right)^{1.4} = \dfrac{P_1}{4.6555}$, so $P_2V_2 = \dfrac{3\times101.3}{4.6555} \approx 65.3$ J.
$$W = \frac{P_1V_1 - P_2V_2}{\gamma - 1} = \frac{101.3 - 65.3}{0.4} \approx 90\ \text{J}$$
The closest option is $90.5$ J.
Solution by Sreeraj P, M.Sc Physics