Radiation Problem: Balancing Net Radiation of Two Spheres

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In summary: The Stefan-Boltzman equation relates the heat flux to the surface temperature of a black body. In this situation, the temperature difference between the two bodies is negligible, so the heat flux is simply proportional to the surface temperature. So the net radiation between them is zero.
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philrainey
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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.
 
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The answer is zero. This is directly from the principle of black body radiation.
 
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Russ, the spheres are at different temperatures. Shouldn't there be a net energy transfer (i.e. not zero)?

philrainey said:
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.
 
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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.
 
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1. What is net radiation?

Net radiation refers to the balance between the amount of incoming radiation (such as heat or light) that is absorbed and the amount that is reflected or emitted by an object or system.

2. How does the net radiation of two spheres affect their temperature?

The net radiation of two spheres determines the amount of heat that is gained or lost by each sphere, which in turn affects their respective temperatures. If the net radiation is positive, the sphere will gain heat and its temperature will increase. If the net radiation is negative, the sphere will lose heat and its temperature will decrease.

3. How can the net radiation of two spheres be balanced?

The net radiation of two spheres can be balanced by adjusting the reflective and emissive properties of each sphere. For example, if one sphere has a higher reflective surface, it will reflect more incoming radiation and thus have a lower net radiation. This can be balanced by increasing the emissivity of the other sphere, allowing it to emit more radiation and have a higher net radiation.

4. What factors can affect the net radiation of two spheres?

The net radiation of two spheres can be affected by several factors, including the difference in their temperatures, their surface properties (reflectivity and emissivity), and the amount of incoming radiation (such as sunlight) they are exposed to.

5. Why is it important to balance the net radiation of two spheres?

Balancing the net radiation of two spheres is important because it allows for a stable and consistent temperature between the two spheres. This is especially important in systems where maintaining a specific temperature is crucial, such as in climate control or thermal regulation in machines or equipment.

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