No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
A polytropic process is one where the pressure and volume of a system are related by the equation PV<sup>n</sup>= C. | A polytropic process is one where the pressure and volume of a system are related by the equation '''PV<sup>n</sup>= C'''. | ||
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: | ||
| Line 10: | Line 11: | ||
These processes have unique shapes (linear, hyperbolic, etc.)depending on the polytropic index. Both open and closed systems can follow polytropic paths. | |||
These processes have unique shapes (linear, hyperbolic, etc.). Both open and closed systems can follow | |||
== Polytropic Index == | == Polytropic Index == | ||
Revision as of 05:13, 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.)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.