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|align="center"|PV<sup>-1</sup>= C | |align="center"|PV<sup>-1</sup>= C | ||
|align="center"| | |align="center"|Work and Heat flow in/out | ||
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| | |Entropy (Isentropic) | ||
|align="center"|γ | |align="center"|γ | ||
|align="center"|PV<sup>γ</sup>= C | |align="center"|PV<sup>γ</sup>= C | ||
|align="center"| | |align="center"|Expansion Valves | ||
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== | For isentropic processes, n = γ = C<sub>p</sub>/C<sub>v</sub>, where C<sub>p</sub> is the heat capacity of an ideal gas at constant pressure, and C<sub>v</sub> is the heat capacity of an ideal gas at constant volume. | ||
Revision as of 05:09, 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.
The equation can also be written as: PVn= K and as P=K/Vn, where Vnis the volume. To find the specific volume this term needs to be divided by the mass.
For specific volume:
P= K/m / Vn/m
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.