Q 11-11-166JEE MainJEE Main 2018 (8 Apr)Medium
Two moles of an ideal monoatomic gas occupies a volume $V$ at $27^\circ$C. The gas expands adiabatically to a volume $2V$. Calculate (a) the final temperature of the gas and (b) change in its internal energy.
Answer: (D) (a) $189$ K (b) $-2.7$ kJ
Adiabatic: $TV^{\gamma - 1} = $ constant with $\gamma - 1 = \dfrac23$:
$$T_2 = 300\left(\frac12\right)^{2/3} = \frac{300}{1.587} \approx 189\ \text{K}$$
$$\Delta U = nC_v\Delta T = 2\times\frac32\times8.31\times(189 - 300) \approx -2.7\ \text{kJ}$$
(The gas does work and cools, so its internal energy falls.)
Solution by Sreeraj P, M.Sc Physics