Question

Work done to increase the temperaure of one mole of an ideal gas by ${30}^o$C, if it is expanding under the condition $V\propto T^{2/3}$ is:

$(R=8.314J/mole{/}^{o}K)$.

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

Answer 1

Answer: (C)

$166.2J$

Given, $V\propto T^{2/3}$ or $V=c{T}^{2/3}$

$dV=c\left(\frac{2}{3}\right)T^{-1/3}dT$

For one mole ideal gas equation:

$PV=RT$

or $P=\frac{RT}{V}=\frac{RT}{c{T}^{2/3}}$

So, work done:

$W=PdV=\frac{RT}{c{T}^{2/3}}\times c\left(\frac{2}{3}\right)T^{-1/3}=\frac{2}{3}RdT=\frac{2}{3}\times 8.314\times 30=166.28J$