Polytropic process

A polytropic process is a thermodynamic process that obeys the relation: A polytropic process is a thermodynamic process that obeys the relation: where p is the pressure, V is volume, n is the polytropic index , 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: Where γ {displaystyle gamma } is the ratio of the heat capacity at constant pressure ( C P {displaystyle C_{P}} ) to heat capacity at constant volume ( C V {displaystyle C_{V}} ). For an ideal gas in a closed system undergoing a slow process with negligible changes in kinetic and potential energy the process is polytropic, such that where C is a constant, K = δ q δ w {displaystyle K={frac {delta q}{delta w}}} , γ = c p c v {displaystyle gamma ={frac {c_{p}}{c_{v}}}} , and with the polytropic coefficient n = ( 1 − γ ) K + γ {displaystyle n={(1-gamma )K+gamma }} .