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

By Stefen's Iaw we use
`P=Ae sigmaT^(4)`
`rArr` `P=Ae sigma (400)^(4)`…(1)
when length and breadth is reduced to half, area becomes `(1)/(4)` times,
Let rate of emission is P'
`p' = A'e sigma(600)^(4)`
`rArr``P'=(A)/(4) e sigma(600)^(4)` ...(2)
Dividing (1) by (2), we get
`(P')/(P)=(Aesigma(600)^(4))/(4) xx (1)/(Ae sigma(400)^(4))`
`rArr(P')/(P) =(81)/(4 xx 16)`
`rArr``P' =(81)/(64)P`