Adiabatic invariance and the ideal gas adiabatic law
The conventional derivation of the ideal gas adiabatic law
PVgamma = constant
involves complex, non-intuitive arguments based on differences between specific heats at constant volume and constant pressure.
A new, intuitive derivation has been developed, based on the behavior of a particle bouncing elastically between two approaching walls. This derivation is in:
The derivation should be useful for a freshman physics class.