MHT CET20227 Aug 2022Evening ShiftPhysicsThermal Properties of MatterActual
Two solid spheres of radii R₁ and R₂ made of same material and have similar surfaces. The spheres are raised to the same temperature and then allowed to cool under identical conditions. Assuming spheres to be perfect conductors of heat, then the ratio of initial rates of cooling are
Options
- Aarray r R₁^2 R₂^2 array
- BR₁^4 R₂^4
- CR₂^3 R₁^3
- DR₂ R₁
Correct answer
A. array r R₁^2 R₂^2 array
Step-by-step solution
According to Stefan's law, we know that: Q= A T^4 e where, area of sphere, A=4 R^2 . Here, temperature, thermal conductivity and emissivity of material are same. So, we get the relation: Q R^2 Initial rate of cooling is given as: Q₁ Q₂ = R₁^2 R₂^2