An ideal gas is taken through a process in which the pressure and the volume are changed according to the equation `p=kv`. Show that the molar heat capacity of the gas for the process is given by `(C=C_v + ( R)/(2))`.

Explanation

`P = KV`
implies `(nRT)/V =KV` implies `RT =KV^(2)`
implies `RDeltaT = 2KVDeltaV`
implies `(RDeltaT)/(2KV)` = DeltaV`
`dQ= dU + dW`
implies `msdT= C_vdT + PdV`
implies `msdT =C_vdT +(PRdT)/(2KV)`
implies `ms = C_v + (RKV)/(2KV)` therefore `C_p = C_v + R/2`