Question

For an ideal gas, consider only P-V work in going from an initial state X to the final state Z. The final state Z can be reached by either of the two paths shown in the figure. Which of the following choice(s) is/are correct? [Take $\Delta S$ as change in entropy and W as work done]

• A. $\Delta S_{X\to Z}$ = $\Delta S_{X\to Y}+\Delta S_{Y\to Z}$
• B. $W_{X\to Z}$ = $W_{X\to Y}+W_{Y\to Z}$
• C. $W_{X\to Y\to Z}\ne W_{X\to Y}$
• D. $\Delta S_{X\to Y\to Z}$ = $\Delta S_{X\to Y}$

Answer 1

The correct option is A $\Delta S_{X\to Z}$ = $\Delta S_{X\to Y}+\Delta S_{Y\to Z}$

$\Delta S$ is a state function. Therefore, it can be calculated as:

$\Delta S_{X\to Z}=\Delta S_{X\to Y}+\Delta S_{Y\to Z}$

While work is a path function.

$\therefore w_{X\to Z}\ne w_{X\to Y}+w_{Y\to Z}$

Also, $w_{X\to Y}=0$ (constant volume)

$\therefore w_{X\to Y\to Z}=w_{X\to Y}$