Polytropic process

A polytropic process is a thermodynamic process that obeys the relation:

where p is the pressure, v is specific volume, n is the polytropic index (a real number), and C is a constant. The polytropic process equation can describe multiple expansion and compression processes which include heat transfer.

If the ideal gas law applies, a process is polytropic if and only if the ratio (K) of energy transfer as heat to energy transfer as work at each infinitesimal step of the process is kept constant:

Some specific values of n correspond to particular cases:

In addition, when the ideal gas law applies:

Consider an ideal gas in a closed system undergoing a slow process with negligible changes in kinetic and potential energy. For an infinitesimal step of time, the first law of thermodynamics states that the energy added to a system as heat δq, minus the energy that leaves the system as work δw, is equal to the change in the internal energy du of the system:

Define the energy transfer ratio,

Transfer of work to the environment can be expressed as ${\displaystyle {\delta w}=p{dv}}$ and internal energy change as ${\displaystyle du=nc_{\,v}\,dT}$

...
Wikipedia