# What is the radiation density in a spherical oven? Does this pertain to the universe? [closed]

Imagine a spherical oven with radius R. The inside of the spherical wall is at temperature T (everywhere) and is assumed emit perfect black body radiation (everywhere).

(1) What is the energy density in the interior of the oven?

(2) Is the energy density homogeneous or does it depend on the radius?

Klaus-Frank

I wonder whether the radiation density of the universe can be described in this way, i.e., as result of a "hot" horizon. Of course, in this case there is the additional issue that the horizon ("oven wall") is growing with time.

## closed as off-topic by StephenG, Aaron Stevens, Yashas, user191954, ahemmetterApr 30 at 7:47

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• Homework-type questions are generally off-topic without reasonable effort being made by the OP. It does not have to be homework as-in-school, it can be also cover self-study and curiosity type questions. – StephenG Apr 29 at 21:29
• I was wondering wether the radiation density of the universe can be understood as result of the temperature of the horizon. I added the explanation. – Klaus-Frank Apr 30 at 4:37

The answer to (1) is that the energy density is $$4\sigma T^4/c$$, where $$\sigma$$ is the Stefan-Boltzmann constant, $$T$$ is the absolute temperature, and $$c$$ is the speed of light. A derivation can be found here. Note that the oven radius $$R$$ is irrelevant as far as the energy density is concerned.
$$\sigma=\frac{2\pi^5k^4}{15c^2h^3},$$
where $$k$$ is Boltzmann’s constant and $$h$$ is Planck’s constant.