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For an ideal gas, consider only P-V work in going from an initial...

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 ΔS as change in entropy and w as work done].


ΔSx→z=ΔSx→y+ΔSy→z
wx→z=wx→y+wy→z
wx→y→z=wx→y
ΔSx→y→z=ΔSx→y
Solution:
ΔSX→Z=ΔSX→Y+ΔSY→Z [Entropy is a state function, hence additive]

wX→Y→Z=wX→Y [Work done in Y→Z is zero because it is an isochoric process].