A polytropic process is one where the pressure and volume of a system are related by the equation PV^{n}= 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= (P_{2}V_{2}-P_{1}V_{1})/(1-n)
Where P_{2}V_{2} and P_{1}V_{1} 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[edit | edit source]
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) | PV^{1}= C | Non-insulated systems |
Pressure (Isobaric) | 0 (unless saturated) | PV^{0}= C | Pistons/Cylinders |
Volume (Isochoric) | ∞ | PV^{∞}= C | Rigid containers |
Linear | -1 | PV^{-1}= C | Work and Heat flow in/out |
Entropy (Isentropic) | γ | PV^{γ}= C | Expansion Valves |
For isentropic processes, n = γ = C_{p}/C_{v}, where C_{p} is the heat capacity of an ideal gas at constant pressure, and C_{v} is the heat capacity of an ideal gas at constant volume.