How much work is done per cycle by a gas following the$P_V$ trajectory of FIGURE EX$21.11$?

When a gas expands , it does work against external pressure . When it contracts , work is done on the gas . When volume remains constant , there is no work done by the gas . When pressure of the gas is constant , work done by gas can be found by the following expression .

Work done $=P∆V$

P is pressure and $∆V$is change in volume . In case both pressure and volume changes , work done by gas can be calculated by calculating the area of graph between P and V .

Area of triangle can give the value of work done by the gas.

Area of triangle $=\frac{1}{2}\times base\times height=\frac{1}{2}\times changeinvolume\times changeinpressure$

Change in volume $=(600-200)\times {10}^{-6}{m}^3=4\times {10}^{-4}{m}^3$

Change in pressure $=(3-1)bar=2\times {10}^{5}Pa$

.The work will therefore be

$W=\frac{2·{10}^5·4·{10}^{-4}}{2}=40\mathrm{J}$

.The work is done by gas equal to$40J$