The rectangular surface area 12cm`xx`6cm of a black body at a temperature of `127^(@)C`, emits heat energy at the rate of Q units per second. If the length and breadth of the surface area are each reduced to half of its initial value and the temperature is increased to `327^(@)C`, then the rate of emission of heat energy will be

Options

A. `81/16Q`
B. `81/32Q`
C. `81/64Q`
D. `9/4xxQ`

Answer

C

Explanation

`(Q/t)=sigmaAT^(4)`
`therefore((Q/t)_(2))/((Q/t)_(1))=(A_(2)/A_(1))xx(T_(2)/T_(1))^(4)`
`" "=((6xx3)/(12xx6))xx((327+273)/(127+273))^(4)`
`" "=1/4xx(600/400)^(4)=1/4xx(3/2)^(4)=81/64`
`therefore(Q/t)_(2)=(81/64)(Q/t)_(1)`