Abstract
An analysis is carried out involving reversible thermodynamic operations on arbitrarily shaped small cavities in perfectly conducting material. These operations consist of quasistatic deformations and displacements of cavity walls and objects within the cavity. This analysis necessarily involves the consideration of Casimir-like forces. Typically, even for the simplest of geometrical structures, such calculations become quite complex, as they need to take into account changes in singular quantities. Much of this complexity is reduced significantly here by working directly with the change in electromagnetic fields as a result of the deformation and displacement changes. A key result of this work is the derivation that for such cavity structures, classical electromagnetic zero-point radiation is the appropriate spectrum at a temperature of absolute zero to ensure that the reversible deformation operations obey both isothermal and adiabatic conditions. In addition, a generalized Wien displacement law is obtained from the demand that the change in entropy of the radiation in these arbitrarily shaped structures must be a state function of temperature and frequency.
Similar content being viewed by others
REFERENCES
D. C. Cole, “Reinvestigation of the thermodynamics of blackbody radiation via classical physics,” Phys. Rev. A 45, 8471-8489 (1992).
D. C. Cole, “Entropy and other thermodynamic properties of classical electromagnetic thermal radiation,” Phys. Rev. A 42, 7006-7024 (1990).
D. C. Cole, “Derivation of the classical electromagnetic zero-point radiation spectrum via a classical thermodynamic operation involving van der Waals forces,” Phys. Rev. A 42, 1847-1862 (1990).
D. C. Cole, “Connection of the classical electromagnetic zero-point radiation spectrum to quantum mechanics for dipole harmonic oscillators,” Phys. Rev. A 45, 8953-8956 (1992).
D. C. Cole, “Reviewing and extending some recent work on stochastic electrodynamics,” in Essays on Formal Aspects of Electromagnetic Theory, A. Lakhtakia, ed. (World Scien-tific, Singapore, 1993), pp. 501-532.
T. H. Boyer, “Scaling symmetry and thermodynamic equilibrium for classical electro-magnetic radiation,” Found. Phys. 19, 1371-1383 (1989).
D. C. Cole, “Classical electrodynamic systems interacting with classical electromagnetic random radiation,” Found. Phys. 20, 225-240 (1990).
D. C. Cole, “Connections between the thermodynamics of classical electrodynamic systems and quantum mechanical systems for quasielectrostatic operations,” Found. Phys. 29, 1819-1847 (1999).
F. M. Serry, D. Walliser, and G. J. Maclay, “The role of the Casimir effect in the static deflection and stiction of membrane strips in microelectromechanical systems (MEMS),” J. Appl. Phys. 84(5), 2501-2506 (1998).
S. Haroche and J._M. Raimond, “Cavity quantum electrodynamics,” Sci. Am. 268(4), 26-33 (1993).
S. Haroche and D. Kleppner, “Cavity quantum electrodynamics,” Phys. Today 42(1), 24_30 (1989).
C. I. Sukenik, M. G. Boshier, D. Cho, V. Sandoghdar, and E. A. Hinds, “Measurement of the Casimir_Polder force,” Phys. Rev. Letts. 70(5), 560-563 (1993).
H. M. Franco, T. W. Marshall, and E. Santos, “Spontaneous emission in confined space according to stochastic electrodynamics,” Phys. Rev. A 45, 6436-6442 (1992).
P. W. Milonni, The Quantum Vacuum. An Introduction to Quantum Electrodynamics (Academic, San Diego, 1994).
L. de la Peña and A. M. Cetto, The Quantum Dice—An Introduction to Stochastic Electro-dynamics (Kluwer Academic Publishers, 1996) and references therein.
T. H. Boyer, “Quantum zero-point energy and long-range forces,” Ann. Phys. 56, 474-503 (1970).
T. H. Boyer, “Quantum electromagnetic zero-point energy of a conducting spherical shell and the Casimir model for a charged particle,” Phys. Rev. 174, 1764-1776 (1968).
J. Ambjoø rn and S. Wolfram, “Properties of the vacuum. I. Mechanical and thermo-dynamic,” Ann. Phys. 147, 1-32 (1983).
H. B. G. Casimir, “Introductory remarks on quantum electrodynamics,” Physica 19, 846-848 (1953).
J. C. Slater, Microwave Electronics (Van Nostrand, New York, 1950).
H. B. G. Casimir, “The theory of electromagnetic waves in resonant cavities,” Philips Res. Rep. 6, 162-182 (1951).
T. H. Boyer, “Random electrodynamics: The theory of classical electrodynamics with classical electromagnetic zero-point radiation,” Phys. Rev. D 11, 790-808 (1975).
D. C. Cole and A. Rueda, Book Review: “The quantum dice: An introduction to stochastic electrodynamics,” Found. Phys. 26, 1559-1562 (1996).
T. H. Boyer, “General connection between random electrodynamics and quantum electro-dynamics for free electromagnetic fields and for dipole oscillator systems,” Phys. Rev. D 11, 809-830 (1975).
D. Kupiszewska, “Casimir effect in absorbing media,” Phys. Rev. A 46, 2286-2294 (1992).
M. J. Renne, “Microscopic theory of retarded van der Waals forces between macroscopic dielectric bodies,” Physica 56, 125-137 (1971).
E. M. Lifshitz, “The theory of molecular attractive forces between solids,” Soviet Phys.– JEPT 2, 73-83 (1956). This is an English translation of Zh. Eksperim. i. Teor. Fiz. 29, 94 (1955).
M. J. Renne, “Retarded van der Waals interaction in a system of harmonic oscillators,” Physica 53, 193-209 (1971).
T. H. Boyer, “Retarded van der Waals forces at all distances derived from classical electro-dynamics with classical electromagnetic zero-point radiation,” Phys. Rev. A 7, 1832-1840 (1973).
D. C. Cole, “Correlation functions for homogeneous, isotropic random classical electro-magnetic radiation and the electromagnetic fields of a fluctuating classical electric dipole,” Phys. Rev. D 33, 2903-2915 (1986).
M. Planck, The Theory of Heat Radiation (Dover, New York, 1959). This publication is an English translation of the second edition of Planck's work entitled Waermestrahlung, published in 1913. A more recent republication of this work is Vol. 11 of the series The History of Modern Physics 1800–1950 (AIP, New York, 1988).
J. D. Jackson, Classical Electrodynamics, 3rd edn. (John Wiley, New York, 1999), Eq. (6.122). 1866 Cole
D. C. Cole, “Cross-term conservation relationships for electromagnetic energy, linear momentum, and angular momentum,” Found. Phys. 29, pp. 1673-1693 (1999), Sec. 4.
S. K. Lamoreaux, “Demonstration of the Casimir force in the 0.6 to 6.0 μ m range,” Phys. Rev. Lett. 78, 5-8 (1997).
U. Mohideen and A. Roy, “Precision measurement of the Casimir force from 0.1 to 0.9 μm,” Phys. Rev. Lett. 81(21), 4549-4552 (1998).
A. Roy and U. Mohideen, “Demonstration of the nontrivial boundary dependence of the Casimir force,” Phys. Rev. Lett. 82(22), 4380-4383 (1999).
A. A. G. Driskill-Smith, D. G. Hasko, and H. Ahmed, “The nanotriode: a nanoscale field-emission tube,” Applied Physics Lett. 75(18), 2845-2847 (1999).
D. C. Cole, “Relating Work, Change in Internal Energy, and Heat Radiated for Dispersion Force Situations,” Proceedings, Space Technology and Applications International Forum–2000 (STAIF 2000), AIP, Vol. 504, M. S. El-Genk, ed., pp. 960-967 (2000).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cole, D.C. Thermodynamics of Blackbody Radiation Via Classical Physics for Arbitrarily Shaped Cavities with Perfectly Conducting Walls. Foundations of Physics 30, 1849–1867 (2000). https://doi.org/10.1023/A:1003706320972
Issue Date:
DOI: https://doi.org/10.1023/A:1003706320972