Polytropic process

From Glossary of Meteorology

polytropic process

A thermodynamic process in which changes of pressure p and density ρ are related according to the formula
where λ is a constant and subscript zeros denote initial values of the variables.

Therefore 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 = cp/R, where cp 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.