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Question
A solid sphere and a hollow sphere of the same material and of equal radii are heated to the same temperature.
(a) Both will emit equal amount of radiation per unit time in the biginning
(b) Both will absorb equal amount of radiation from the surrounding in the biginning.
(c) The initial rate of cooling (dT/dt) will be the same for the two spheres
(d) The two spheres will have equal temperature at any instant
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Solution
(a) Both will emit equal amount of radiation per unit time in the beginning.
(b) Both will absorb equal amount of radiation from the surrounding in the beginning.
Let the temperature of the surroundings be T0
From the Stefan-Boltzmann law, the energy of thermal radiation emitted per unit time by a blackbody of surface area A is given by `u = σAT^4`
Here, σ is Stephen's constant.
Also, the energy absorbed per unit time by the body is given by
`u_0 = eσAT_0^4`
As the two spheres have equal radii and temperatures, their rate of absorption and emission will be equal in the beginning.
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