# Polytropic process

From Glossary of Meteorology

## polytropic process

A thermodynamic process in which changes of pressure where λ is a constant and subscript zeros denote initial values of the variables.

*p*and density ρ are related according to the formulaTherefore pressure and temperature are similarly related: where

*k*is the coefficient of polytropy. For isobaric processes,*k*= 0; for isosteric processes,*k*= 1; for adiabatic processes*k*=*c*_{p}/*R*, where*c*_{p}is the specific heat at constant pressure and*R*is the gas constant; sometimes applied to circumstances when adiabatic heating or cooling combine with slow ascent or descent to produce a particular lapse rate. In meteorology this formula is applied to individual air parcels and should be distinguished from that for a polytropic atmosphere, which describes a distribution of pressure and temperature in space.*See also*equation of piezotropy.