Q 11-12-029JEE MainJEE Main 2026 (5 Apr, Shift 2)Medium
An ideal gas at pressure $P$ and temperature $T$ is expanding such that $PT^3 =$ constant. The coefficient of volume expansion of the gas is ______.
Answer: (C) $\dfrac{4}{T}$
Concept. Coefficient of volume expansion $\gamma=\dfrac1V\dfrac{dV}{dT}$. Combine the given relation with $PV=nRT$ to get $V$ as a power of $T$.
Step 1. Eliminate $P$. $P=\dfrac{nRT}{V}$, so $PT^3=\dfrac{nRT^4}{V}=$ constant, i.e. $V\propto T^4$.
Step 2. Coefficient. $\dfrac1V\dfrac{dV}{dT}=\dfrac4T$.
Answer. Option C. In general $V\propto T^k$ gives $\gamma=\dfrac kT$.
Solution by Sreeraj P, M.Sc Physics
