A thermodynamic system is taken through the cycle abcda. The work done by the gas along the path bc is :

In the given PV diagram the thermodynamic cycle is traced as a → b → c → d → a. The segment b → c appears as a **vertical line** on the diagram, which means that the volume of the gas does **not change** during this part of the process.

Work done by a gas in a quasi‑static process is expressed by
$W\; =\; \backslash int\_\{V\_i\}^\{V\_f\}\; P\backslash ,dV$.

Because the volume is constant ($V\_i\; =\; V\_f$) for the path b → c, the differential $dV$ is zero at every point, and therefore

$W\_\{bc\}\; =\; \backslash int\_\{V\}^\{V\}\; P\backslash ,dV\; =\; 0$.

Hence, the work done by the gas along the path b c is **zero**.