Physics – Classical Physics
Scientific paper
2002-10-30
Am. J. Phys. 71, 866-870 (2003).
Physics
Classical Physics
10 pages
Scientific paper
10.1119/1.1566782
A thermodynamic analysis of the harmonic oscillator is presented. Motivation for the study is provided by the blackbody radiation spectrum; when blackbody radiation is regarded as a system of noninteracting harmonic oscillator modes, the thermodynamics follows from that of the harmonic oscillators. Using the behavior of a harmonic oscillator thermodynamic system under a quasi-static change of oscillator frequency w, we show that the thermodynamic functions can all be derived from a single function of w/T, analogous to Wien's displacement theorem. The high- and low-frequency energy limits allow asymptotic energy forms involving T alone or w alone, corresponding to energy equipartition and zero-point energy. It is noted that the Planck spectrum with zero-point radiation corresponds to the function satisfying the Wien displacement result which provides the smoothest possible interpolation between energy equipartition at low frequency and zero-point energy at high frequency.
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