For an ideal gas, consider only P-V work in going from an initial state $\mathrm{X}$ to the final state…
For an ideal gas, consider only P-V work in going from an initial state $\mathrm{X}$ to the final state $\mathrm{Z}$. The final state $\mathrm{Z}$ can be reached by either of the two paths shown in the figure. Which of the following choice(s) is (are) correct?
[Take $\Delta \mathrm{S}$ as change in entropy and w as work done].
$\mathrm{w}_{x \rightarrow y \rightarrow z}=\mathrm{w}_{x \rightarrow y}$
$\Delta \mathrm{S}_{x \rightarrow y \rightarrow z}=\Delta \mathrm{S}_{x \rightarrow y}$
Solution
$\Delta S_{X \rightarrow Z}=\Delta S_{X \rightarrow Y}+\Delta S_{Y \rightarrow Z}$ [Entropy is a state function, hence additive]
$w_{X \rightarrow Y \rightarrow Z}=w_{X \rightarrow Y}$ [Work done in $Y \rightarrow Z$ is zero because it is an isochoric process].
