Polytropic process

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 = 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.

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