The polytropic process is one in which the pressure-volume relation is given as
The exponent n may have any value from minus infinity to plus infinity depending on the process. Some of the more common values are given below.
Process |
Exponent n |
Constant pressure |
0 |
Constant volume |
¥ |
Isothermal & ideal gas |
1 |
Adiabatic & ideal gas |
k = C_{P}/C_{V} |
Here k is the ratio of the specific heat at constant pressure, C_{P}, to specific heat at constant volume, C_{V}. The specific heats will be discussed later.
The boundary work done during the polytropic process is found by substituting the pressure volume relation into the boundary work equation. The result is
For an ideal gas under going a polytropic process the boundary work is
Notice that the results we obtained for an ideal gas undergoing a polytropic process when n = 1, is identical to that for an ideal gas undergoing the isothermal process.