Explanation:
Formula for black body radiation is as follows.
[tex]\frac{P}{A} = \sigma \times T^{4} J/m^{2}s[/tex]
where, P = power emitted
A = surface area of black body
[tex]\sigma[/tex] = Stephen's constant = [tex]5.6703 \times 10^{-8} watt/m^{2}.K^{-4}[/tex]
As area is given as 1.0 [tex]cm^{2}[/tex]. Converting it into meters as follows.
[tex]1.00 cm^{2} \times \frac{(10^{-2})^{2} m^{2}}{1 cm^{2}}[/tex] (as 1 m = 100 cm)
= [tex]1 \times 10^{-4} m^{2}[/tex]
It is given that P = 201 watts. Hence,
[tex]\frac{201 watts}{1 \times 10^{-4} m^{2}}[/tex] = [tex]5.6703 \times 10^{-8} watt/m^{2}.K^{-4} \times T^{4}[/tex]
[tex]T^{4}[/tex] = [tex]35.45 \times 10^{12}[/tex]
T = [tex](35.45 \times 10^{12})^{1/4}[/tex]
= 8862.5 K
Thus, we can conclude that the temperature of the surface is 8862.5 K.
