Q 11-11-097JEE MainJEE Main 2023 (1 Feb, Shift 1)Medium
A sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is (given $\gamma=\frac32$)
Answer: (D) $W=RT(2-\sqrt2)$
For one mole, $TV^{\gamma-1}=$ constant gives $T_2=T\left(\dfrac12\right)^{1/2}=\dfrac{T}{\sqrt2}$.
$$W=\frac{R(T_1-T_2)}{\gamma-1}=2RT\left(1-\frac1{\sqrt2}\right)=RT(2-\sqrt2)$$
Solution by Sreeraj P, M.Sc Physics