Question

For an ideal gas, consider only P-V work is given 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 a 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. $\Delta W_{X\to Z}=\Delta W_{X\to Y}+\Delta W_{Y\to Z}$
• C. $\Delta W_{X\to Y\to Z}=\Delta W_{X\to Y}$
• D. $\Delta S_{X\to Y\to Z}=\Delta S_{X\to Y}$

Answer 1

Answer: (A), (C)

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

Entropy is a state function. Its value is independent of the path followed.

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

Hence, option A is correct and option D is incorrect.

Work is a path function. Its value depends on the path followed.

$\Delta W_{X\to Y\to Z}=\Delta W_{X\to Y}$

This is because $\Delta W_{Y\to Y}=0$ as the volume change from Y to Z is zero.

Thus, option C is correct and option B is incorrect.