Polytropic process

Equivalence between the polytropic coefficient and the ratio of energy transfers

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 $${\displaystyle p{v}^{(1-\gamma )K+\gamma }=C}$$ where C is a constant, ${\displaystyle K=\frac{\delta q}{\delta w}}$, ${\displaystyle \gamma =\frac{c_p}{c_v}}$, and with the polytropic coefficient ${\displaystyle n=(1-\gamma )K+\gamma }$.

Relationship to ideal processes

For certain values of the polytropic index, the process will be synonymous with other common processes. Some examples of the effects of varying index values are given in the following table.

When the index n is between any two of the former values (0, 1, γ, or ∞), it means that the polytropic curve will cut through (be bounded by) the curves of the two bounding indices.

For an ideal gas, 1 < γ < 5/3, since by Mayer's relation $${\displaystyle \gamma =\frac{c_p}{c_v}=\frac{c_v+R}{c_v}=1+\frac{R}{c_v}=\frac{c_p}{c_p-R}.}$$

Other

A solution to the Lane–Emden equation using a polytropic fluid is known as a polytrope.

The term "polytropic poison" has been used exclusively in publications from Russia regarding lead poisoning and chloroprene to indicate multisystemic toxic effects.

In entomology it has been used to denote insects visiting various flowers for nectar.