Today in astrophysics tutorial one of my students asked my how I could
show that black body radiation pressure obeys the ideal gas law:
P V = N k T
where P = pressure, V = volume, N = number of photons, k = Boltzmann's
constant, and T = temperature. I asked him where he had got that
relation. He said at first he thought it was in the textbook, but then
he decided I had said it in lecture yesterday. I said that I didn't
think I'd said it, but I would look into it. Of course the dimensions
are OK so the equation might hold apart from a numerical constant.
In preparation fopr tomorrow's lecture I worked out the result tonight.
I was astonished to calculate that blackbody radiation exerts a
pressure P which obeys the law:
P V = 0.902 <N> k T
which is *close* to the ideal gas law, but far enough away that I am
confident it's not the same. The fact that the constant is nearly
unity is a surprise to me. (<N> is the average number of photons.)
Has anyone out there seen this relation before? Have I calculated
something that everyone knows already? Have I blown the calculation?