A gas at constant pressure of \(4.0 \times 10^{5} Pa\) is cooled so that its volume decreases form \(1.6 m ^{3}\) to \(1.2 m ^{3}\). What work is performed by the gas?
A. \(6.4 \times 10^{5} J\) B. \(3.2 \times 10^{5} J\) C. \(1.6 \times 10^{5} J\) D. \(0.4 \times 10^{5} J\)
Correct Answer: C
Explanation
Workdone by the gas is given as \(P\left(V-V_{0}\right)\) $$ \begin{aligned} W &=\int P d v=P \int d v=P \times\left. V\right|_{v_{0}} ^{v} P \Delta V \\ W &=4 \times 10^{5} \times(1.6-1.2) \\ &=1.6 \times 10^{5} J \end{aligned} $$
