For an ideal gas, an illustration of three different paths A, (B +C) and (D+E) from an initial state `P _(1) , V _(1), T _(1)` to a final state `P _(2), V _(2), T _(1)` is shown in the given

Path A represents a reversible isothermal expansion from `P _(1), V _(1), ` to `P _(2), V _(2)` Path (B +C) represents a reversible adiabatic expansion (B) from `P _(1), V _(1), T _(1)` to `P _(3), V _(2) , T _(2)` followed by reversible heating the gas at constant volume (C) from `P _(3), V _(2), T _(2)` to `P _(2), V _(2), T _(1).` Path (D+E) represents a reversible expansion at constant pressure `P _(1)` from `P _(1) , V _(1), T _(1)` to `P _(1), V _(2), T _(3)` followed by a reversible cooling at constant volume `V _(2) (E)` frm `V _(1) , V _(2) T _(3)` to` P _(2) , V _(2), T _(1).`
What is `Delta S` for path A ?

Options

A. `- P ( V _(2) - V _(1))`
B. `- n R ln"" ( V _(2))/(V _(1))`
C. `+ P ( V _(2) - V _(1))`
D. `n R ln "" (V_(2))/(V _(1))`

Explanation

For path (D+E) ,` Delta S = n R ln "" ( V _(2))/(V _(1))`