Adiabatic invariance and its application to Wien's complete displacement law of blackbody radiation

Abstract

We derive the “complete” or “strong” version of Wien's displacement law from two adiabatic invariants: one of a thermodynamic system composed of a finite-sized segment of frequencies taken from the spectrum of blackbody radiation and one of the individual electromagnetic waves that compose this system. By exploiting the algebra of these invariants, we shift the calculational burden of deriving Wien's displacement law toward the methods of classical thermodynamics. These methods also produce a class of displacement laws that constrain both the particles of a classical ideal gas and the acoustic waves of the Debye model of a solid.