Polytropic
Definition
... a process that exhibits the following relationship
$$ p V^n = constant $$
, denoted by a curve on the pV diagram and a curve on a Ts diagram.
Where it occurs.
In place of isentropic compressions/ expansions, whenever a heat leak/ gain is evident.
Special features
There is a finite heat addition or heat rejection. Note that the polytropic relationship is not a physical law. It follows from observations. It happens in some processes, but by no means all processes. For example, an expansion/ compression in a spring-piston-cylinder arrangement is not a polytropic process.
How to draw it
Locate the POI and press the polytropic button.
The theory
There are some special values for n. Setting \( n = 0 \) gives constant pressure. Setting \( n = 1 \) gives Boyle's law, \( pV = constant \) for constant
temperature. Setting \( n = \gamma \) gives isentropic expansion/ compression.
Exercises
Click on the graph to get a POI and plot an polytropic curve through it. Using the same POI, replicate constant pressure with n-0, isotherms with n=1, and isentropic with n = 1.4. Note how the gradient increases with n.
Links
Christians' approach.