Radiation Problem: Balancing Net Radiation of Two Spheres

[philrainey]

I was trying to work out a question where there is a little sphere inside a big sphere with a perfect vacuum inbetween.the big sphere been 0.13m dia. and 1550 degrees kelvin hot. The little sphere .1m dia. and 1500 degrees kelvin. All of the radiation from the little sphere hits the big but some from the big misses the small and hits itself.What is the net radiation between them ? Do you think you can work out the percentage of radiation that hits the small sphere from the big is proportional to the amount of angle that hits the little sphere from a point on the big sphere divided by 180 degrees?Both spheres are black bodies.

 

[russ_watters]

The answer is zero. This is directly from the principle of black body radiation.

 

[Redbelly98]

Russ, the spheres are at different temperatures. Shouldn't there be a net energy transfer (i.e. not zero)?

Do you think you can work out the percentage of radiation that hits the small sphere from the big is proportional to the amount of angle that hits the little sphere from a point on the big sphere divided by 180 degrees?Both spheres are black bodies.

It wouldn't work that way, for two reasons:

1. We are dealing with http://en.wikipedia.org/wiki/Solid_angle" here, with units of square degrees or steradians. "180 degrees" does not represent the solid angle of a hemisphere.
2. The radiated intensity follows a cos(θ) distribution. So at larger angles from the normal, the intensity is less.

 

[philrainey]

Oh I see I did not know about the cos(x) distribution that is very interesting. I was hoping on my incorrect thinking of even distribution that there would be a net transfer from the cold body to the hot (yes I know this is suppose to be impossible) But we do a lot of things today that 100 years ago seemed impossible. Cheers. Perhaps if the hot body was a star shape with the cold body in the middle away from the perpendicular radiation.

 

[russ_watters]

Sorry, misread - thought it said 1550 for both.

Anyway, you don't really need angles to do such a problem, you just need the Stefan-Boltzman equation: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html