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QPages 96-97: Q6: HC Verma: Concepts of Physics - Volume 2 Heat Transfer Pages 96-97: Q6 Solution: Two identical metal balls one at and the other at are kept at a …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often apply the Stefan‑Boltzmann law as $P_{net}=\sigma A\,(T_2^4\! -\! T_1^4)$, assuming the two bodies exchange heat only with each other. In vacuum each sphere also radiates to empty space, and the fraction of one sphere’s emission that reaches the other is given by the view factor (≈$A/(4\pi d^2)$ for small spheres). Ignoring this geometry leads to the false belief that the temperatures will equalise and that the heat gain is simply proportional to $T_2^4-T_1^4$.

Two identical metal balls one at T1=300 KT_1 = 300 \text{ K} and the other at T2=600 KT_2 = 600 \text{ 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 T24−T14T_2^4 - T_1^4 as may be expected from the Stefan's law?

Step-by-Step Verified Solution

**Answer:** No, the temperatures will not equalize by radiation. No, the rate of heat gained by the colder sphere is not proportional to T__ _ T__. **Step-by-Step Explanation:** Both spheres radiate energy in all directions, but each receives only a fraction of the radiation emitted by the other. The energy lost by radiation is much greater than the energy received. Therefore, both spheres will cool down, and their temperatures will not equalize. The rate of heat gained by the colder sphere is not proportional to T__ _ T__ because the area through which heat is lost differs from the area on which heat is gained [citation:13].

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