One mole of a gas is in state `A[P, V, T_(A)]`. A small adiabatic process causes the state of the gas to change to `B [P + dP, V + dV, T_(B)]`. The changes dV & dP are infinitesimally small and dV is negative. An alternative process takes the gas from state A to B via `A rarr C rarr B`. `A rarr C` is isochoric and `C rarr B` is isobaric path. State at C is `[P + dP, V, T_(C)]`.
(a) Rank the temperatures `T_(A), T_(B)` and `T_(C)` from highest to lowest.
(b) Find g of the gas in terms of `T_(A)`, `T_(B)` and `T_(C)`.

Answer

(a) `T_(C) gt T_(B) gt T_(A)` , (b) `gamma = (T_(C)-T_(A))/(T_(C)-T_(B))`