For the ideal gas, consider P-V work in going from an initial state X to final state Z. The final state ‘Z’ can be reached by either of the two paths as shown in the figure. Which of the following choices are correct? (Take $Δ S$ as entropy change , $Δ G$ as free energy change and W as work done)

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$Δ S_{x \to z} = Δ S_{x \to y} + Δ S_{y \to z}$

$Δ G_{x \to z} = Δ G_{x \to y} + Δ G_{y \to z}$

$W_{x \to y \to z} = W_{x \to y}$

$Δ S_{x \to y \to z} = Δ S_{x \to y}$

answer is A, B, C.

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Detailed Solution

a) $Δ S_{x - z} = Δ S_{x - y} + Δ S_{y - z}$
b) $Δ G_{x - z} = Δ G_{x - y} + Δ G_{y - z}$ because $Δ S$ and $Δ G$ are state functions
c) $W_{x \to y \to z} = W_{x - y} (b e c a u s e W_{y - z} = 0)$ (as it is isochoric process)
d) $Δ S_{x \to y \to z} \neq Δ S_{x \to y}$ but it is $Δ S_{x - y} + Δ S_{y - z}$