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For an ideal gas, consider only \( \mathrm{P}-\mathrm{V} \) 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 \( \mathrm{w} \) as work done]
(A) \( \Delta \mathrm{S}_{x \rightarrow 2}=\Delta \mathrm{S}_{x \rightarrow y}+\Delta \mathrm{S}_{y \rightarrow z} \)
(B) \( \mathrm{W}_{x \rightarrow 2}=\mathrm{W}_{x \rightarrow y}+\mathrm{W}_{y \rightarrow z} \)
(C) \( \mathrm{W}_{x \rightarrow y \rightarrow z}=\mathrm{W}_{\mathrm{x} \rightarrow y} \)
(D) \( \Delta \mathrm{S}_{\mathrm{x} \rightarrow \mathrm{y} \rightarrow z}=\Delta \mathrm{S}_{\mathrm{x} \rightarrow \mathrm{y}} \)
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