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## Homework Statement

Raising the temperature of 1[itex]cm^{3}[/itex] of water (1 gram, water has a heat cap. of 4.2 J/g*K) using energy from a cavity filled with black body radiation. The water is to change from 299K to 300K. The radiation is initially at 450K.

If the cavity has a volume of 0.1 [itex]m^{3}[/itex] how long would you need to have the heating coils turned on to heat the water? (voltage of coils is 240V, and current is 20A)

## Homework Equations

P=IV

Energy of a photon gas = ([itex]\frac{8\pi^{5}*k^4}{15c^3*h^3}[/itex])V[itex]T^{4}[/itex]

radiative flux = [itex]\sigma[/itex][itex]T^{4}[/itex] sigma is stefan-boltzmann constant

## The Attempt at a Solution

I want to say that the energy input from the coils should be enough and the time would be 4.2J /480V*20A, but that can't be it. Honestly I'm totally lost on this one because the radiative flux would require that you know a surface area, but one is not given (and maybe that the volume doesn't even matter), any thoughts?