# Kirchoff's law of radiation (very confused )

1. Jan 12, 2006

### sachi

kirchoff's law of radiation (very confused!!)

we have a large evacuated enclosure which is black on the inside maintained at a constant temperature T0. there are two black spheres suspended within the enclosure close but not touching and sphere A is maintained at temperature T1 (T1>T0). when B is at T0 the rate of loss of heat from A is W1 and when B is at T1 the rate of loos of heat from A is W2. show that there is no loss of heat from A when B is at T2 where

(T2)^4 = W1/(W1-W2) * ((T1)^4 - (T0)^4) + (T0)^4

I know that in the enclosure the energy density (due to the walls) is A(T0)^4 and that the power absored by sphere A is sigma(T0)^4 *surface area where sigma is stefan's constant. I'm having trouble finding the energy absorbed due to B. Do we assume that because they are close the intensity of radiation due to B does not decrease on its way to A? What proportion of A's surface area is illuminated by this radiation (is it just the cross sectional area?) Also, do we need to know the areas of the two spheres? Thanks for your help