AP EAMCET202021 Sep 2020Evening ShiftPhysicsThermal Properties of MatterActual
A rectangular metal plate (8 ~cm 4 ~cm ) at (127^ C ) emits (E Js ⁻¹ ). If both length and breadth are halved and the temperature is raised to (327^ C ), the rate of emission is
Options
- A( ( 9 4 ) E Js ⁻¹ )
- B( ( 81 64 ) E Js ⁻¹ )
- C( ( 27 8 ) E Js ⁻¹ )
- D( ( 10 7 ) E Js ⁻¹ )
Correct answer
B. ( ( 81 64 ) E Js ⁻¹ )
Step-by-step solution
According to Stefan-Boltzmann's law, rate of emission of radiation from metal surface is given as, ( aligned E & = A T^4 E₂ E₁ & = ( A₂ A₁ ) ( T₂ T₁ )^4 (i) aligned ) ( aligned Given, A₁ & =8 ~cm 4 ~cm & =3.2 10⁻³ ~m ^2 T₁ & =127+273=400 ~K A₂ & = 8 2 ~cm 4 2 ~cm & =4 2 ~cm ^2=8 10⁻⁴ ~m ^2 T₂ & =327+273=600 ~K aligned ) Putting these values in Eq. (i), we have ( aligned & E₂ E₁ = ( 8 10⁻⁴ 3.2 10⁻³ ) ( 600 400 )^4 & = 1 4 81 16 & E₂ E₁ = 81 64 & E₂= 81 64 E₁= ( 81 64 ) E Js ⁻¹ [ E₁=E Js ⁻¹ ] aligned )