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This Insight develops equations of state that are useful in calculations about cosmology and about the insides of stars. The first calculation is for a photon gas and the second is for a ‘relativistic’ gas of particles with mass.
Photon Gas
Exercise 22 on p108 of Bernard Schutz’s ‘A first course in General Relativity’ (Second Edition) is to prove that, for an isotropic, monochromatic, photon gas, p=ρ/3, where p is pressure and ρ is mass-energy density.
Say all photons have frequency ##\nu## and the number of photons per cubic metre is ##n##. Then ##\rho=n h \nu##.
Now consider one face of a cube of side length 1m. The pressure on that face is the component, parallel to the normal to the face, of the impulse delivered to that face in one second, by photons striking it from outside the cube. We can ignore components of impulse that are parallel to the face, because the isotropy will make such components from different particles cancel each other out.
We measure that impulse by...
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