Polytropic process

A process which occurs with an interchange of both heat and work between the system and its surroundings. The nonadiabatic expansion orcompression of a fluid is an example of a polytropic process. The interrelationships between the pressure (P) and volume (V) and pressureand temperature (T) for a gas undergoing a polytropic process are given by Eqs. (1) and

(1) 

(2) 

(2), where a and b are the polytropic constants for the process of interest. These constants, which are usually determined from experiment,depend upon the equation of state of the gas, the amount of heat transferred, and the extent of irreversibility in the process. See Isentropic process, Isothermal process, Thermodynamic processes.

Polytropic Process

 a change in the state of a physical system where the system’s specific heat C remains constant. The curve representing a polytropic processon a thermodynamic diagram is called a polytropic curve.

A simple example of a reversible polytropic process is the polytropic change of an ideal gas. This process is defined by the equation pVⁿ=const, where p is the pressure of the gas, V is the volume of the gas, and n = (C— C_P)/(C— Cv) is the polytropic exponent (Cp and Cv are thespecific heats of the gas at constant pressure and constant volume, respectively). By using the equation of state for an ideal gas, the equationof a polytropic curve can be written in a different form: pT^n/(1-n)= const or VT^1(1-n) = const, here T is the absolute temperature. Special casesof the equation of a polytropic process for an ideal gas are the equations for an isentropic curve, where C = 0 and n = C_p/cv (this ratio ofspecific heats is designated γ); an isobar, where C— C_p and n = 0; an isochor, where C= Cv and n = ∞; and an isotherm, where C= ∞ and n =1. The work A done by an ideal gas against the ambient pressure is determined from the formula

where the subscripts 1 and 2 refer to the initial and final states of the gas.

Engineering thermodynamics makes extensive use of the concept of polytropic processes in investigating the operating cycles of heatengines."Pantropic" redirects here. For the term used in distributions, see pantropical.

Thermodynamics
The classical Carnot heat engine

A polytropic process is a thermodynamic process that obeys the relation:

where p is the pressure, v is specific volume, n, the polytropic index, is any real number, and C is a constant. The polytropic process equation is particularly useful for characterizing expansion and compression processes which include heat transfer. This equation can accurately characterize a very wide range of thermodynamic processes, that range from n=0 to n= which covers, n=0 (isobaric), n=1 (isothermal), n=γ (isentropic), n= (isochoric) processes and all values of n in between. Hence the equation is polytropic in the sense that it describes many lines or many processes. In addition to the behavior of gases, it can in some cases represent some liquids and solids. The one restriction is that the process should display an energy transfer ratio of K=δQ/δW=constant during that process. If it deviates from that restriction it suggests the exponent is not a constant. For a particular exponent, other points along the curve can be calculated: