A black rectangular surface of area A emits energy E per second at `27^circC`. If length and breadth are reduced to initial value and temperature is raised to `327^circC`, then energy emitted per second becomes

Options

A. `(4E)/9`
B. `(7E)/9`
C. `(10E)/9`
D. `(16E)/9`

Answer

A

Explanation

According to question, `E=e sigma A(T^4-T_0^4)` [where symbols have their usual meanings]
When l and b change to `l/3` and `b/3` pue respectively.
Area becomes `l/3xxb/3xx(lb)/3xx=A/3` `(because A=lb)`
Now for two different cases
`E^'/E=A^'/A(227+373)^4/(27+273)^4=1/9(600/300)^4`
`therefore E^'/E=1/9xx(2)^4xxE RightarrowE^'=(16E)/9`