Thermodynamics of the Harmonic Oscillator: Derivation of the Planck Blackbody Spectrum from Pure Thermodynamics

TL;DR

This paper demonstrates that the Planck blackbody spectrum, including zero-point energy, can be derived solely from classical thermodynamics applied to harmonic oscillators, without quantum mechanics or statistical assumptions.

Contribution

It shows that the third law of thermodynamics suffices to derive the Planck spectrum with zero-point energy from classical thermodynamics.

Findings

The Planck spectrum can be obtained from thermodynamics alone.

Zero-point energy inclusion aligns naturally with thermodynamic principles.

Classical thermodynamics provides a complete understanding of blackbody radiation.

Abstract

In 1893, Wien applied the first two laws of thermodynamics to blackbody radiation and derived his displacement theorem. Believing that the information from thermodynamics had been exhausted, Planck turned to statistical ideas in 1900 in order to provide a physical understanding for his experimental--data-based interpolation giving the Planck spectrum without zero-point radiation. Here we point out that the third law of thermodynamics (which was developed in the early years of the 20th century) introduces additional thermodynamic information regarding thermal radiation. The Planck spectrum for thermal radiation can be derived from purely thermodynamic ideas applied to the classical simple harmonic oscillator, since every radiation mode takes a simple oscillator form. Thermodynamics alone implies the Planck spectrum including zero-point energy without any need for quantum theory or statistical ideas. It is pointed out that the inclusion of zero-point energy involves more natural thermodynamics than its exclusion.