(a) A polytropic process for an ideal gas is represented by `PV^(x) =` constant, where `x != 1`. Show that molar specific heat capacity for such a process is given by `C = C_(v) + (R)/(1-x)`.
(b) An amount Q of heat is added to a mono atomic ideal gas in a process in which the gas performs a work `(Q)/(2)` on its surrounding. Show that the process is polytropic and find the molar heat capacity of the gas in the process.

Answer

`PV^(1//3)` =constant ; C=3R