Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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Two Identical Metal Balls One at T1 = 300 K and the Other at T2 = 600 K Are Kept at a Distance of 1 M in a Vacuum. - Physics

Short Note

Two identical metal balls one at T1 = 300 K and the other at T2 = 600 K are kept at a distance of 1 m in a vacuum. Will the temperatures equalise by radiation? Will the rate of heat gained by the colder sphere be proportional to `t_2^4 - t_1^4` as may be expected from the Stefan's law?

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Solution

Yes, the temperature of the balls can be equalised by radiation. This is because both the spheres will emit radiations in all the directions at different rates.
The ball kept at the temperature of 300 K will gain some thermal energy by the radiation emitted by the ball kept at the temperature of 600 K. Also, it losses energy by radiation.
Similarly, the ball kept at the temperature of 600 K will gain some thermal energy by the radiation emitted by the ball kept at the temperature of 600 K. Also, it losses energy by radiation.
A time comes when the temperature of both the bodies becomes equal.

Yes, the rate of heat gained by the colder sphere is proportional to `t_2^4 - t_1^4`.

Concept: Heat Transfer - Radiation
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APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 6 Heat Transfer
Short Answers | Q 6 | Page 97
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