A polytropic process is described by the formula , where . The table below shows the association of different pV curves for ideal gases with the corresponding thermodynamic processes:

###### Question

Why is the projection an adiabat when and why is a constant when ?

###### Answer

From eq44 and eq46, and for an ideal gas. For adiabatic processes, and hence, . Furthermore, . Since , . So,

which rearranges to , where .

For the second why, . If , .