Find equation for thermodynamic process

1. The problem statement, all variables and given/known data

Find the equation of the thermodynamic process in which specific heat of the gas is given by



[itex]C=\dfrac{R}{\gamma -1} + \alpha P [/itex]





3. The attempt at a solution



I can write



[itex]C=C_v + \alpha P [/itex]



But I don't know how to proceed ahead. Any help is appreciated.