Q 11-11-035JEE MainJEE Main 2026 (8 Apr, Shift 2)Medium
Initial pressure and volume of a monoatomic ideal gas are $P$ and $V$. The change in internal energy of this gas in adiabatic expansion to volume $V_{\text{final}} = 27V$ is ______ J.
Answer: (C) $-\dfrac{4}{3}PV$
For a monoatomic gas $\gamma = \dfrac{5}{3}$. Adiabatic: $P_fV_f^\gamma = PV^\gamma$:
$$P_f = P\left(\frac{1}{27}\right)^{5/3} = \frac{P}{243}, \qquad P_fV_f = \frac{P}{243} \times 27V = \frac{PV}{9}$$
$\Delta U = nC_v\Delta T = \dfrac{3}{2}(P_fV_f - PV) = \dfrac{3}{2}\left(\dfrac{1}{9} - 1\right)PV = -\dfrac{4}{3}PV$.
Solution by Sreeraj P, M.Sc Physics