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 beginning.
B. Both will absorb equal amount of radiation from the surrounding in the beginning.
C. The initial rate of cooling (dT/dt) will be the same for the two spheres.
D. The two spheres will have equal temperatures at any instant.
According to Stefan- Boltzmann Law:
The energy of thermal radiation emitted per unit time by a body having surface area A is given as:
Here, e (between 0 to 1) is the emissivity of the body and σ is the Stefan-Boltzmann constant and T is the Temperature.
Since the spheres have equal radii and are of same material, the area of cross section would be same for both the spheres.
Thus Stefan’s Law will hold true for both the spheres in the exact same way. Hence, both will emit equal amount of radiation per unit time in the beginning.
The energy of radiation absorbed by the spheres should be equal to the energy of radiation emitted by them. Applying same Stefan-Boltzmann
Law we get,
Where u0 is the energy of radiation absorbed and T0 is the initial surrounding temperature.
Again due to equal Area of cross section and same material, both will absorb equal amount of radiation from the surrounding in the beginning.
Thus, options (a) and (b) are the correct options.
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