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. `DeltaS_(XrarrZ)=DeltaS_(XrarrY) + DeltaS_(xrarrz)`
B. `W_(xrarrz) = W_(x rarry) + W_(yrarrz)`
C. `W_(xrarr yrarrz) = W_(xrarry)`
D. `DeltaS_(xrarryrarrz) = DeltaS_(xrarry)`

Answer

A, C

Explanation

`{:((A) DeltaS_(xrarr2) = DeltaS_(x-y) + DeltaS_(yrarrz) ,("correct")),((B)W_(xrarry)=W_(x-y) + W_(y-z) , ("Incorrect")),((C)W_(xrarr yrarrz)=W_(x-y),("correct")),((D)DeltaS_(xrarr yrarr z) = DeltaS_(x-y),("Incorrect")):}`