A black body maintained at a certain temperature radiates heat energy at the rate `Q` watt. If its surface is smoothened so as to lower its emissivitiy by 10%, what will be the increase in its rate of radiation at double the initial temperature?

Options

A. `(0.9xx102^(4)-1)Q` watt
B. `0.9xx2^(4)Q` watt
C. `(0.9xx2)^(4)Q` watt
D. `(0.9)^(4)xx2Q` watt

Explanation

(a) For a black body,
Rate of radiation `Q=sigmaT^(4)`
After smoothing and doubling the temperature `=`Rate `Q`
`=0.9sigma(2T)^(4)=0.9xx10^(4)Q`
Charge `=(0.9xx2^(4)-1)Q` watt