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Where P represents the pressure, V represents the volume, n represents the polytropic index, and C is a constant. | 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: | A polytropic process can be related to work by the equation: | ||
Revision as of 05:11, 20 November 2018
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.). Both open and closed systems can follow a polytropic path.
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.