MCQ
For an ideal gas, consider only $P - V$ work in going from an initial state $X$ to the final stat $Z$. 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].

$(A)$ $\Delta S _{ x \rightarrow z}=\Delta S _{ x \rightarrow y}+\Delta S _{ y \rightarrow z}$

$(B)$ $w_{x \rightarrow z}=w_{x \rightarrow y}+w_{y \rightarrow z}$

$(C)$ $w_{x \rightarrow z \rightarrow z}=w_{x \rightarrow y}$

$(D)$ $\Delta S _{x \rightarrow y \rightarrow z}=\Delta S _{x \rightarrow y}$

  • A
    $(A,C)$
  • B
    $(B,C)$
  • C
    $(A,D)$
  • D
    $(C,D)$

Answer

$(A)$ $\Delta S_{x \rightarrow z}=\Delta S_{x-y}+\Delta S_{y \rightarrow z}$

(Correct)

$(B)$ $W _{x \rightarrow y}= W _{x-y}+ W _{ y \rightarrow z }$

(Incorrect)

$(C)$ $W _{x \rightarrow y \rightarrow z}= W _{x-y}$

(Correct)

$(D)$ $\Delta S _{x \rightarrow j \rightarrow z}=\Delta S _{x-y}$

(Incorrect)

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