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

 

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. 

$$\begin{gathered} As is clear from figure, \\ {W}_{AEDA}=+ area of ∆AED=+\frac{1}{2}{P}_0{V}_0 \\ {W}_{BCEB}=-Area of ∆BCD=-\frac{1}{2}{P}_0{V}_0 \end{gathered}$$

The network done by the system is

$W_{\text{net }}=W_{AEDA}+W_{BCEB}$

$=+\frac{1}{2}{P}_0{V}_0-\frac{1}{2}{P}_0{V}_0=\text{ zero }$