Question

A gas expands from an initial pressure $P_1=300$ kPa and volume $V_1=0.05m^3$ to a final pressure $P_2=100$ kPa. If pressure volume relationship during the process is $P{V}^3$ = constant. The work done during the process is ______ kJ.

• A. $5\text{kJ}$
• B. $3.9\text{kJ}$
• C. $1.2\text{kJ}$
• D. $0\text{kJ}$

Answer 1

The correct option is B $3.9\text{kJ}$

$P_1=300kPa;P_2=100kPa;V_1=0.05m^3$

$P{V}^3=const$.

$\Rightarrow$ $\frac{V_2}{V_1}=\sqrt[3]{3\frac{P_1}{P_2}}=\sqrt[3]{3\frac{300}{100}}$

$\Rightarrow$ $V_2=0.05\times \sqrt[3]{33}=0.072m^3$

$\text{Work done,}W=\frac{P_1{V}_1-P_2{V}_2}{3-1}=\frac{300\times 0.05-100\times 0.072}{2}=3.9kJ$