Reinvestigation of the thermodynamics of blackbody radiation via classical physics

Abstract

A key part of the early thermodynamic work on blackbody radiation by Wien, Stefan, Boltzmann, Planck, and others involved the thermodynamic behavior of a movable piston sliding in a cylinder containing classical electromagnetic thermal radiation. This early work used only classical physics concepts. Here, this analysis is reinvestigated with the change that the implicit assumption is not made that the thermal radiation spectrum reduces to zero at the temperature T =0. Previous work has shown that this consideration may be an important one to yield agreement, or at least better agreement, between classical physical theory and the actual physical behavior of molecular, atomic, and subatomic systems in nature. Indeed, the present analysis on "cavity thermodynamics" accounts for the thermodynamic behavior of Casimir forces between the walls of the cavity. Using only the traditional thermodynamic definition of T =0, the form of the classical electromagnetic zero-point (ZP) radiation spectrum is deduced. From the second law of thermodynamics, two forms of Wien's displacement law are obtained and generalized to include the possibility of ZP radiation. The entropy is then explicitly calculated for the parallel-plate case. Also, the limiting situation of high-temperature radiation between the plates and low temperature outside is examined to recover the early analysis by Wien, Planck, and others. Most of the analysis is carried out for two parallel conducting plates bathed in thermal radiation; the Appendix extends this analysis to a rectangular conducting box with a movable interior wall.PACS number(s): 05.90.+m, 03.50.De, 05.40.+ j thermodynamic operations performed upon a cavity containing blackbody radiation. In particular, here the thermodynamic operations are investigated of (i) quasistatically displacing two conducting parallel plates from each other that are bathed in classical electromagnetic thermal radiation, as well as (ii) slowly changing the temperature of the system. The Appendix (see Ref.[16]) indicates how this analysis can be extended to a hollow box with conducting walls, where one of the walls of the box can be displaced. Thus this analysis is closely connected to the early work by researchers around 1900 involving a closed cylinder at some temperature, with a movable pis-45 1992 The American Physical Society 8472 DANIEL C. COLE 45 ton at one end.As we will see, by including the possibility that the thermal radiation spectrum is nonzero at T =0, the classical electromagnetic ZP spectrum of p(co)=@co /c can be deduced strictly from the thermodynamic definition of absolute zero temperature. Other points obtained here include (i) thermodynamically accounting for Casimir forces in the analysis, (ii) derivations of two distinct forms of the Wien displacement law when ZP radiation is present, and (iii) a calculation of the entropy associated with classical electromagnetic thermal radiation between two plates, as a function of both temperature and volume.These last properties have not been found before when Z...

Simulation Results Related to Stochastic Electrodynamics

“…If one examines the thermodynamic issues surrounding this question, particularly as in Refs. [16], [44], [21], and [45], but also as supported and discussed from other perspectives in Refs. [4], [5], and [22], there is nothing contained within the three laws of classical thermodynamics that suggest that ‡uctuating motion for classical systems should not exist for systems of classical charged particles at T = 0.…”

“…References [16], [44], [21], [47], [48], and [22] proved that for the electrodynamic systems investigated, only one spectral functional form of classical electromagnetic radiation conforms with the following thermodynamic de…nition of absolute zero temperature: namely, that no heat should ‡ow during reversible thermodynamic operations. The spectral form deduced was precisely that of classical electromagnetic ZP radiation, with the energy per unit volume per unit angular frequency interval being…”

“…However, as analyzed by Cole in Ref. [21] and discussed more generally in Ref. [80], these early thermodynamic analyses subtly imposed, without possibly intending to, that all radiation vanishes as T !…”

“…0. These derivations can be reconstructed in a very natural way without this assumption [21], thereby enabling one to deduce the functional form of the spectral energy density and its limit as T ! 0 [44], [21], [47], [48], [22].…”

Energy and thermodynamic considerations involving electromagnetic zero-point radiation

“…References (Cole, 1990a) and (Cole, 1990b) discuss other related points that are often cited as a failure of classical physics, such as the ultraviolet catastrophe, infinite specific heat, and the third law of thermodynamics. References (Cole, 1990a), (Cole, 1992a) and (Cole, 1992b) analyze specific classical electrodynamic systems and provide derivations for the classical electromagnetic ZP spectrum, based on the thermodynamic definition of temperature. In this work care is taken to make sure that the implicit assumption that motion and fluctuations reduce to zero at 0 = T is not made in the analysis, as occurred, sometimes inconsistently, at various points in the work by physicists in the early 1900s.…”