What are the conditions of a ideal Stefan-Boltzmann gas?

[florian]

Does anybody know the conditions of a ideal Stefan Boltzmann gas? And the EoS?
thanks a lot
florian

 

[AstroRoyale]

weakly interacting or non-interacting particles are required for the ideal gas. The equation of state for an ideal gas is the ideal gas law:

$$P=\rho k T$$

 

[florian]

I found something like
p = $$\epsilon/3$$
$$\epsilon = \pi^2gT^4$$/30
... is this compatible to your equation?
... is the Stefan-Boltzmann gas the normal ideal gas, or is there an additional condition?
... what is with the mass of the particles? is there any condition to them?
thanks for the responds
regards
florian

 

[AstroRoyale]

If you mean a relativistic gas such as photons, which always travel at the speed of light, then you are on the right track.

$$P = \frac{1}{3}\epsilon$$
where the energy density is $$\epsilon$$. This is the "Equation of state" for a relativistic gas.

and the energy density is $$\epsilon=aT^{4}$$ where a is called the radiation constant $$a=\frac{4\sigma}{c}$$.

The mass could, I suppose be anything, as long as the particles are moving relativistically, although the most common thing we talk about are photons, which are of course massless.
I've personally never heard the term Stephan-Boltzmann gas, there is the Stephan-Boltzmann law though. I think you are talking about a relativistic gas?

 

[florian]

yes i think so too :-)... and which are the conditions? because it is still an ideal gas and not real:
1. I guess no interaction is a condition
2. probably the particles have to be massless...
but my problem is the following: In the books they use this approximation to describe a QGP (quark gluon plasma) or a gas of hadrons... and for both I can't see why the masses should be negligible... in the case of QGP there are the s quark with a mass of 300MeV (u and d are negligible) and in the case of hadrons (approximated as pion gas) I have a mass of 140MeV and the temperature is about 160MeV...
regards
florain

 

[AstroRoyale]

As T > Mass, the particles are certainly relativistic, even if they have mass. Massless particles are just guaranteed to be relativistic. Weak interactions are needed for the ideal gas, probably why the QGP is now thought of more as a fluid than an ideal gas. Dunno, anyone else know more about this?