Abstract
Thermodynamics arguments have been employed to derive how the energy densityρ depends on the temperatureT for a fluid whose pressurep obeys the equation of statep = (γ −1)ρ, whereγ is a constant. Three different methods, among them the one considered by Boltzmann (Carnot cycle), lead to the expressionρ = ηTγ/(γ −1), whereη 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 = −ρ), cosmic strings (p= −1/3ρ), radiation (p = 1/3ρ), and stiff matter (p = ρ). It is also shown that such results can be adapted for blackbody radiation inN spatial dimensions.
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de Lima, J.A.S., Santos, J. Generalized Stefan-Boltzmann law. Int J Theor Phys 34, 127–134 (1995). https://doi.org/10.1007/BF00670992
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DOI: https://doi.org/10.1007/BF00670992