A perfectly black body emits radiation at temperature `T_(1)`K. If is to radiate at 16 times this power, its temperature `T_(2)`K should be

Options

A. `T_(2)=4T_(1)`
B. `T_(2)=8T_(1)`
C. `T_(2)=2T_(1)`
D. `T_(2)=16T_(1)`

Answer

C

Explanation

According to Stefan's law `Q/t=sigmaAT^(4)`
`((Q/t)_(2))/((Q/t)_(1))=(T_(2)/T_(1))^(4)" "therefore16=(T_(2)/T_(1))^(4)`
`thereforeT_(2)/T_(1)=root(4)16=2" "thereforeT_(2)=2T_(1)`