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For an ideal gas, consider only P-V work in going from an initial state \( X \) to the final state \( Z \). The final state \( Z \)
P can be reached by either of the two paths shown in the

W figure. Which of the following choice(s) is (are) correct? [take \( \Delta \mathrm{S} \) as change in entropy and \( \mathrm{w} \) as work done].
(A) \( \Delta \mathrm{S}_{\mathrm{x} \rightarrow \mathrm{z}}=\Delta \mathrm{S}_{\mathrm{x} \rightarrow \mathrm{y}}+\Delta \mathrm{S}_{\mathrm{y} \rightarrow \mathrm{z}} \)
(B) \( w_{x \rightarrow z}=w_{x \rightarrow y}+w_{y \rightarrow z} \)
(C) \( w_{x \rightarrow y \rightarrow z}=w_{x \rightarrow y} \)
(D) \( \Delta S_{x \rightarrow y \rightarrow z}=\Delta S_{x \rightarrow y} \)
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