Problem $7$:

A gas is compressed from an initial volume of $0\mathrm{.}42m^3$ to a final volume of $0\mathrm{.}12m^3.$ During the

quasi$-$equilibrium process, the pressure changes with volume according to the

relation $P=aV+b_{?},$ where $a=-1200kP\frac{a}{m^3}$ and $b=400kP{a}_{?}.$ Calculate the work done during

this process by performing the necessary integration.