Talk:Photon gas

Contradictory Internal Energy Equations
There are two equations given for the internal energy of the gas that differ by a factor of 8*pi^3. Pulu (talk) 15:14, 25 June 2011 (UTC)

They aren't. It's a problem that the page isn't consistent in the use of h vs \hbar. — Preceding unsigned comment added by 99.126.181.250 (talk) 07:00, 3 March 2012 (UTC)

$$U = (8 Pi^5 k^4)/(15 c^3 h^3) V T^4$$

$$N = (2 [Pi] Zeta[3] k^3)/(c^3 [hbar]^3) V T^3$$

$$U = 3 P V$$

$$P V = Zeta[4]/Zeta[3] N k T$$

These 4 equations are not satisfied. Because Zeta[4] = [Pi]^4 / 90, there are [Pi]^3 different. Laoma (talk) 15:20, 10 March 2012 (UTC)laoma


 * Thanks for pointing that out. The expression for N was wrong. It's fixed now. PAR (talk) 01:19, 11 March 2012 (UTC)

This needs to be revisited, because there have been several edits since this discussion. There may be an erroneous factor of $$(2 \pi)^3$$ in the expressions for the number of photons. This all boils down to confusion between $$h$$ and $$\hbar$$. Perhaps the expressions should be given in two forms to reduce likelihood of incorrect future edits, one set in terms of $$h$$ and $$\nu$$ and another set in terms of $$\hbar$$ and $$\omega$$. Hypoon (talk) 19:45, 14 May 2018 (UTC)

I agree with Hypoon. The present expression for N should be an hbar instead of h in the denominator. It presently reads low by a factor of (2 pi)^3. 99.118.236.34 (talk) 03:46, 28 June 2018 (UTC)Chuck Link (talk) 04:35, 28 June 2018 (UTC)

The equation given for the photon density contradicts an equation given by Steven Weinberg in his book "The First Three Minutes".

The equation given here has 16 π k^3 ζ(3) T^3 in the numerator and c^3 h^3 (2 π)^3 in the denominator. In Weinberg's version of this, "(2 π)^3" is missing. Obviously "h^3 (2 π)^3" is "h_quer". The difference between the two equations is significant. How comes nobody has corrected this in 9 years? Sky Darmos (talk) 07:40, 12 April 2019 (UTC)Sky Darmos.


 * are you sure is not a SI-Gaussian units issue?--MaoGo (talk) 09:15, 12 April 2019 (UTC)

I discussed the whole thing in this physics forum:

https://www.physicsforums.com/threads/photon-density-in-photon-gases.970034/

The conclusion is that you guys tried to use 'ℏ' everywhere, so that you had to add '(2π)^3' here. The equation for "U" is also once written with 'ℏ' and then with 'h'. I fixed it already. Sky Darmos (talk) 09:50, 12 April 2019 (UTC)
 * I corrected your last edition because it was right if you compare with the table below. Maybe we should add some source to avoid additional corrections.--MaoGo (talk) 10:58, 12 April 2019 (UTC)
 * I corrected everything to use \hbar all over. Finally, I left 'h' for historical reasons (specially because we use have Plancks law which most people know in its 'hυ' form from their introductory courses). In the table at the bottom we have the ħ formulas MaoGo (talk) 11:58, 12 April 2019 (UTC)

Bose distribution
Not mentioning the Bose distribution here seems perverse. — Preceding unsigned comment added by 86.176.174.4 (talk) 16:44, 4 May 2014 (UTC)