Question

A gas is compressed from an initial volume of 0.42 m3 to a final volume of 0.12 m3. During the quasi-equilibrium process, the pressure changes with volume according to the relation P = aV + b, where a = –1200 kPa/m3 and b = 500 kPa. Calculate the work done during this process (a) by plotting the process on a P-V diagram and finding the area under the process curve and (b) by performing the necessary integrations.

Answer 1

Answer:

$W=-52 800\ \text{J}=-52.8\ \text{kJ}$

Explanation:

First I sketched the compression of the gas with the help of the given pressure change process relation. That is your pressure change due to change in volume.

To find the area underneath the curve (the same as saying to find the work done) you should integrate the given relation for pressure change:

$W=\int_{0.42}^{0.12}-1200V+500dV=-52.8\ \text{kJ}$