Question

Find the amount of work done to increase the temperature of one mole of an ideal gas by ${30}^{o}C$ if it is expanding under the condition $V\propto T^{2/3}$.

• A. $166.2J$
• B. $136.2J$
• C. $126.2J$
• D. none of these

Answer 1

The correct option is A $166.2J$

$PV=RT$ for 1 mole
$W=\int PdV=\int \frac{RT}{V}dV$
$V=C{T}^{2/3}$
$\therefore dV=\frac{2}{3}C{T}^{-1/3}dT$
Dividing dV by V we get
$\frac{dV}{V}=\frac{2}{3}\frac{dT}{T}$
Now Work done is given as
$W={\int }_{T_1}^{T_2}RT\left(\frac{2}{3}\right)\frac{dT}{T}$
$=\frac{2}{3}R(T_2-T_1)=166.2J$