Applicability
The equation is a valid characterization of a thermodynamic process assuming that the process is quasistatic and the values of the heat capacities, and, are almost constant when is not zero or infinity. (In reality, and are actually functions of temperature and pressure, but are nearly constant within small changes of temperature).
Under standard conditions, most gases can be accurately characterized by the ideal gas law. This construct allows for the pressure-volume relationship to be defined for essentially all ideal thermodynamic cycles, such as the well-known Carnot cycle. Note however that there may also be instances where a polytropic process occurs in a non-ideal gas. This is also called the general law of the expansion and compression of gases in non flow processes.
Read more about this topic: Polytropic Process