Work done by gas

Question

A thermodynamic system undergoes cyclic process ABCDA as shown in figure. The work done by the system in the cycle is

Easy

Solution

In a cyclic process work done is equal to the area under the cycle and is positive if the cycle is clockwise and negative if anticlockwise.

$Asisclearfromfigure,\phantom{\rule{0ex}{0ex}}{W}_{AEDA}=+areaof\u2206AED=+\frac{1}{2}{P}_{0}{V}_{0}\phantom{\rule{0ex}{0ex}}{W}_{BCEB}=-Areaof\u2206BCD=-\frac{1}{2}{P}_{0}{V}_{0}$

The network done by the system is

${W}_{\text{net}}={W}_{AEDA}+{W}_{BCEB}$

$=+\frac{1}{2}{P}_{0}{V}_{0}-\frac{1}{2}{P}_{0}{V}_{0}=\text{zero}$

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