MHT CET20243 May 2024Morning ShiftPhysicsThermal Properties of MatterActual
Two spherical black bodies of radii ' R₁ ' and ' R ₂ ' and with surface temperature ' T ₁ ' and ' T ₂ ' respectively radiate the same power. The ratio of ' R₁ ' to ' R₂ ' will be
Options
- A( T₂ T₁ )^4
- B( T₂ T₁ )^2
- C( T₁ T₂ )^4
- D( T₁ T₂ )^2
Correct answer
B. ( T₂ T₁ )^2
Step-by-step solution
For any two bodies of radii R₁ and R₂ , kept at temperatures T₁ and T₂ , the power radiated or rate of loss of heat by them can be given as, Q ₁ Q ₂ = ( R ₁ R ₂ )^2 ( T ₁ ~T ₂ )^4 In case of non-spherical bodies, ( R ₁ R ₂ )^2 can be replaced by ( A₁ A₂ ) where A₁, A₂ are areas of the given bodies. For same power, aligned & ( R ₁ R ₂ )^2= ( T ₂ ~T ₁ )^4 & ( R ₁ R ₂ )= ( T ₂ ~T ₁ )^2 aligned