A solid sphere and a hollow sphere are made of the same material and have equal outer radii. Both are heated to the same temperature and then allowed to cool. Which statement is correct in the beginning?

Both emit equal amounts of radiation per unit time initially
Both absorb equal amounts of radiation from the surroundings initially
The initial rate of temperature fall (dT/dt) is the same for both spheres
The two spheres remain at equal temperatures at every later instant

Correct answer: Both emit equal amounts of radiation per unit time initially

Solution

Emission rate depends only on surface area, emissivity and temperature, all equal here, so both emit equally at first; but the hollow sphere has less mass, so it cools faster (dT/dt differs).

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