(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The density of the energy of radiation in a cavity at temperature T is [tex]u(T) = aT^4[/tex]. Suppose the cavity is a sphere whose radius increases at a rate of:

[tex]\frac{dr}{dt} = v_0[/tex]

Assuming that no energy enters or leaves the enclosure, will the temperature increase or decrease, and if so, at what rate?

2. Relevant equations

All given in the problem, I believe.

3. The attempt at a solution

I was thinking that intuitively as the sphere gets bigger the temperature would have to go down because the distribution of radiation would be more spread throughout, but then again that's just a guess at best.

I was thinking that u(T) = E/V since it's just energy density, but I can't really much get much farther than that. I also thought that perhaps obtaining [tex]\frac{dV}{dt} = 4\pi*r^2*v_0[/tex] might be useful later on but I don't know how.

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# Homework Help: Question with energy density

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