A polytropic process is one where the pressure and volume of a system are related by the equation PVn= C.

Where P represents the pressure, V represents the volume, n represents the polytropic index, and C is a constant.

A polytropic process can be related to work by the equation:

W= (P2V2-P1V1)/(1-n)

Where P2V2 and P1V1 represent pressure and volume at two different time-steps of a process.

These processes have unique shapes (linear, hyperbolic, etc.)depending on the polytropic index. Both open and closed systems can follow polytropic paths.

## Polytropic Index

Polytropic processes are usually categorized either by what variable remains constant in the process, or by the shape of its corresponding graph (e.g. linear)

When n is less than 0: Negative n values represent a large amount of heat added to the system is much greater than the work done by the system

Constant n Equation Associated with
Temperature (Isothermic) 1 (unless saturated) PV1= C Non-insulated systems
Pressure (Isobaric) 0 (unless saturated) PV0= C Pistons/Cylinders
Volume (Isochoric) PV= C Rigid containers
Linear -1 PV-1= C Work and Heat flow in/out
Entropy (Isentropic) γ PVγ= C Expansion Valves

For isentropic processes, n = γ = Cp/Cv, where Cp is the heat capacity of an ideal gas at constant pressure, and Cv is the heat capacity of an ideal gas at constant volume.

Authors Dion Kucera, Sam Smith CC-BY-SA-3.0 English (en) Russian, Chinese, Persian, Korean, Turkish, Spanish 6 subpages, 9 pages link here 10,753 page views December 3, 2013 by Dion Kucera March 2, 2022 by Page script Dion Kucera, Sam Smith (2013–2022). "Polytropic process". Appropedia. Retrieved July 20, 2024. basic, semantic, html, files, more
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