Adiabatic invariance  


Adiabatic invariants as effective Hamiltonians

P. M. Bellan and R. J. Perkins, Orbit-averaged quantities, the classical Hellmann-Feynman theorem, and the magnetic flux enclosed by gyro-motion, Phys. Plasmas 22, 022108 (2015)

R. J. Perkins and P. M. Bellan, Wheels within Wheels: Hamiltonian Dynamics as a Hierarchy of Action Variables, Phys. Rev. Lett. 105, art 124301 (2010)



Adiabatic invariants and the ideal gas 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:

P. M. Bellan, A microscopic, mechanical derivation of the adiabatic gas relation, American J. Phys. 72,  679 (2004).

The derivation should be useful for a freshman physics class.


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