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) $-\dfrac{4}{3}PV$
Concept. Adiabatic expansion: $PV^\gamma$ constant ($\gamma=\tfrac53$), and $\Delta U=nC_V\Delta T=\tfrac32\Delta(PV)$.
Step 1. Final $PV$. $P_2=P\cdot27^{-5/3}=\dfrac{P}{243}$, so $P_2V_2=\dfrac{27PV}{243}=\dfrac{PV}{9}$.
Step 2. $\Delta U$. $\tfrac32\left(\dfrac{PV}{9}-PV\right)=-\dfrac43PV$.
Answer. Option C.
Solution by Sreeraj P, M.Sc Physics
