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Question:

For an ideal gas, consider only P-V work. 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?

ΔSX→Z=ΔSX→Y+ΔSY→Z

ΔWX→Y→Z=ΔWX→Y

ΔSX→Y→Z=ΔSX→Y

ΔWX→Z=ΔWX→Y+ΔWY→Z

Solution:

Entropy is a state function. Its value is independent of the path followed. Therefore, the change in entropy from state X to state Z is the same regardless of the path taken. This means ΔSX→Z = ΔSX→Y + ΔSY→Z is correct. Work, however, is a path function. The work done depends on the path taken. Therefore, ΔWX→Y→Z ≠ ΔWX→Z.