The rectangular surface of area `8 cm xx 4 cm` of a black body at temperature `127^(@)C` emits energy `E` per section if length and breadth are reduced to half of the initial value and the temperature is raised to `327^(@)C`, the ratio of emission of energy becomes

Options

A. `(3)/(8)E`
B. `(81)/(16)E`
C. `(9)/(16)E`
D. `(81)/(64)E`

Answer

D

Explanation

Energy radiated by body per second `(Q)/(t)Asigma T^4`
or `(Q)/(t)proplxxbxxT^4` (Area `= l xx b`)
`:. (E_2)/(E_1)=(l_2)/(l_1)xx(b_2)/(b_1)xx((T_2)/(T_1))^4=((l_(1)//2))/(l_(1))xx((b_(1)//2))/(b_(1))xx((600)/(400))^4`
`=(1)/(2)xx(1)/(2)xx((3)/(2))^4impliesE_2=(81)/(64)E`