Q 11-11-008JEE MainEAMCET 2012 (Engineering)Hard
The work done to increase the temperature of one mole of an ideal gas by $30°$C, if it is expanding under the condition $V \propto T^{2/3}$, is ($R = 8.314$ J/mol K)
Answer: (A) $166.3$ J
$V \propto T^{2/3}$ and $PV \propto T$ give $PV \propto V^{3/2}$, i.e. $P \propto V^{1/2}$: a polytropic process $PV^x = $ constant with $x = -\dfrac{1}{2}$.
$$W = \frac{nR\Delta T}{1 - x} = \frac{8.314 \times 30}{1.5} \approx 166.3\ \text{J}$$
Solution by Sreeraj P, M.Sc Physics