Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer
A solid sphere and a hollow sphere made of the same material and having equal radii are heated to an identical temperature.
Options
- AThe two spheres will possess equal temperatures at any given instant.
- BThe initial rate of cooling ( dT/dt ) will be equal for the two spheres.
- CIn the beginning, both will emit an equal amount of radiation per unit time.
- DIn the beginning, both will absorb an equal amount of radiation from the surroundings.
Correct answer
D. In the beginning, both will absorb an equal amount of radiation from the surroundings.
Step-by-step solution
The rate of emission of radiation by a body is given by Stefan-Boltzmann law: E = e A T^4 Since both the solid and hollow spheres have the same radius, their surface areas A are equal. Being made of the same material, their emissivities e are equal. As their initial temperatures T are identical, both spheres will emit an equal amount of radiation per unit time in the beginning. The rate of absorption of radiation from the surroundings is given by: P_ abs = a A T₀^4 where T₀ is the temperature of the surroundings an