Polytropic process

Remarks

For an ideal gas with constant heat capacity ratio $\gamma$, the special cases are as follows. The index $n = 0$ gives an isobaric process. The index $n = 1$ gives an isothermal process, since a constant product $pV$ means a constant temperature for an ideal gas. The index $n = \gamma$ gives a reversible adiabatic, hence isentropic, process. In the limit $n \to \infty$ one gets an isochoric process. For $n \ne 1$, the work done by the fluid from $(p_1, V_1)$ to $(p_2, V_2)$ is $(p_1 V_1 - p_2 V_2) / (n - 1)$. A process with $p = a + bV$ for constants $a, b \ne 0$ is not polytropic, since $p V^n$ is not constant along it for any $n$.