Register to reply 
The equation of state of radiation 
Share this thread: 
#1
Oct1609, 09:09 AM

P: 54

Why does the EOS of radiation set to 1/3? Where does this come from?



#2
Oct1609, 10:07 AM

Sci Advisor
HW Helper
P: 1,275

Heuristic argument:
P = N * F/A P = N * dp_x/dt / A P = N * dp_x / (L / v_x) / A And v^2 = v_x^2 + v_y^2 + v_z^2 = 3v_x^2 > v = sqrt(3) v_x We can make a similar argument for the components of momentum to get an overall factor of 3. P = N/V * <pv> / 3 Then for a photon gas <pv> is the energy, so we have P = Energy per particle * Number / Volume / 3 = energy density / 3 Another way I have seen it derived, is to take the EM Stress tensor, show that it must be traceless, and compare that with the general identity (for a perfect fluid) [tex]T^{\mu}_{\mu} = \rho + 3p[/tex] 


#3
Oct1609, 08:44 PM

P: 54

If there is a layer of photon gas surrounding a black hole‘s surface, will the pressure of this gas still be isotropic? In other words, the energy tensor is still
[tex]\begin{display} T^{\mu}_{\nu}=\left( \begin{array}{cccc} \rho & 0 & 0 & 0 \\ 0 & p & 0 & 0 \\ 0 & 0 & p & 0 \\ 0 & 0 & 0 & p \\ \end{array} \right) \end{display}[/tex] , isn't it? Or the g11 is not equal to g22,g33 any more? 


#4
Oct1709, 04:02 PM

Sci Advisor
HW Helper
P: 1,275

The equation of state of radiation
I would think so, but I'm not terribly certain.



#5
Oct2309, 04:33 AM

P: 54

Does somebody know that which book gives the detail derivation of this formula—the energymomentum tensor of radiation, namely
[tex] \begin{display} T^{\mu}_{\nu}=\left( \begin{array}{cccc} \rho & 0 & 0 & 0 \\ 0 & p & 0 & 0 \\ 0 & 0 & p & 0 \\ 0 & 0 & 0 & p \\ \end{array} \right) \end{display} [/tex] ? 


#6
Oct2309, 05:11 AM

Sci Advisor
P: 1,253

That is actually the form for any perfect fluid (i.e. one in which we can neglect viscosity and voritcity). Any GR textbook will have some amount of explanation about the derivation of this. I find 'Gravitation' by Hartle an excellent introductory textbook, but others will have this info also.



Register to reply 
Related Discussions  
Equation for S from state func and C  Advanced Physics Homework  1  
Equation of state of an electron gas  Atomic, Solid State, Comp. Physics  2  
Isotropic Radiation Equation  Electrical Engineering  3  
The equation of state  Cosmology  2  
Van der Waal's equation of state  Introductory Physics Homework  3 