MHT CET202311 May 2023Evening ShiftPhysicsThermal Properties of MatterActual
Two bodies A and B at temperatures ' T ₁ ' K and ' T ₂ ' K respectively have the same dimensions. Their emissivities are in the ratio 1: 3 . If they radiate the same amount of heat per unit area per unit time, then the ratio of their temperatures (T₁: T₂ ) is
Options
- A1: 3
- B3^ 1 / 4 : 1
- C9^ 1 / 4 : 1
- D81: 1
Correct answer
B. 3^ 1 / 4 : 1
Step-by-step solution
From Stefan - Boltzmann's law dQ dt = e ( AT ^4 ) Given A and dQ dt are same for both the bodies gathered e ₁ ~T ₁^4= e ₂ ~T ₂^4 ( T ₁ ~T ₂ )^4= e ₂ e ₁ = 3 1 T ₁ ~T ₂ = [4] 3 1 = 3^ 1 4 1 gathered