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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 S as change in entropy and w as work done]


A
SXZ=SXY+SYZ
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B
wXZ=wXY+wYZ
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C
wXYZwXY
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D
SXYZ=SXY
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Solution

The correct option is A SXZ=SXY+SYZ
As S does not depend on path and only depends on initial and final state of the system i.e., it is a state function thus SXZ=SXY+SYZ

As we know that work is not a state function and depends on path,
Thus, wXZwXY+wYZ

wXY=PdV (P is constant)
wYZ=0 (as V is constant)

wXYZ=wXY+wYZ
As wYZ=0,hence wXYZ=wXY

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