A polytropic process is one where the pressure and volume of a system is related by the equation PVn= C. Such processes are defined by what is constant in the process.
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 shapes, and some of these shapes have names (such as linear, hyperbolic, etc.). Both open and closed systems can follow a polytropic path.
Polytropic Index
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 |
---|---|
Temperature | 1 |
Pressure | 0 |
Volume | ∞ |
Linear | -1 |
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.