Question

Work done to increase the temperature of one mole of an ideal gas by $30^{\circ }C$, if it is expanding under the condition $V\propto T^{2/3}$ is, $(R=8.314J/mol/K)$

• A. 116.2 J
• B. 136.2 J
• C. 166.2 J
• D. 186.2 J

Answer 1

Answer: (C)

We have, $V\propto T^{2/3}$
and $p\propto \sqrt{V}$
$\therefore p=k\sqrt{V}$
$\Rightarrow p=k{V}^{1/2}$
Work done, $W=\int pdV$
$W=\int k{V}^{1/2}$
$W=\frac{k{V}^{3/2}}{3/2}$
$W=\frac{2}{3}\frac{p}{\sqrt{V}}{V}^{3/2}=\frac{2}{3}pV\left[\because V=\frac{p}{\sqrt{V}}\right]$
$=\frac{2}{3}nRT=\frac{2}{3}\times 1\times 8.3\times 30=166.2J$