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
Such processes are defined by what is constant in the process.
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
When n is equal to 0: A constant pressure, or isobaric process
When n is equal to 1: A constant temperature, or isothermal process
When n is equal to infinity: Volume is constant, this is an isochoric process
| Constant | n | Explanation | Association |
|---|---|---|---|
| Temperature | 1 (unless saturated) | A constant temperature, or isothermal, polytropic process is modeled by the equation PV1= C | |
| Pressure | 0 (unless saturated) | ||
| Volume | ∞ | ||
| Linear | -1 | ||
| Heat and mass flow | γ |
Isentropic Process
An isentropic process is a particular type of polytropic process, whereby n is the heat capacity ratio of an ideal gas and the system contains that ideal gas.