Generalized Stefan-Boltzmann law |
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Authors: | J. A. S. de Lima J. Santos |
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Affiliation: | (1) Departamento de Física, Universidade Federal do Rio G. do Norte, C. Postal 1641, 59072-970 Natal-RN, Brazil |
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Abstract: | Thermodynamics arguments have been employed to derive how the energy density depends on the temperatureT for a fluid whose pressurep obeys the equation of statep = ( –1), where is a constant. Three different methods, among them the one considered by Boltzmann (Carnot cycle), lead to the expression = T/( –1), where is a constant. This result also appears naturally in the framework of general relativity for spacetimes with constant spatial curvature. Some particular cases are vacuum (p = –), cosmic strings (p= –1/3), radiation (p = 1/3), and stiff matter (p = ). It is also shown that such results can be adapted for blackbody radiation inN spatial dimensions. |
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