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.

# Discussion

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