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Consider a gas of non-interacting bosons associated with the energy spectrum
where h and c are constants, and k is a wave vector. Calculate the pressure of this gas at zero chemical potential. What is the pressure of radiation of a gas of photons?
Physics
In the thermodynamic limit we have
In zero chemical potential, it is easy to show that
Note that the pressure of radiation is given by the equation of state
pV = 1/3
Taking into account the law of Stefan-Boltzmann, U = σV T4, we obtain an expression for the constaT σ.
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