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 `DeltaS` as change in entropy and `w` as work done]

Options

A. `Delta S_(x rarr z) = Delta S_(x rarr y) + Delta S_(y rarr z)`
B. `W_(x rarr z) = W_(x rarr y) + W_(y rarr z)`
C. `W_(x rarr y rarr z) = W_(x rarr y)`
D. `Delta S_(x rarr y rarr z) = Delta S _(x rarr y)`

Answer

A, C, D

Explanation

`Delta S_(x rarr z) = Delta S_(x rarr y) + Delta S _(Y + z)` [Enthropy (S) is a state fuction, hecne additive] `W_(X rarr Y rarr Z) = W_(X rarr Y)` (work done in `Y rarr Z` is zero as it is an isochoric process)