Question

What maximum power can be radiated by a 10-cm-diameter solid lead sphere? Assume an emissivity of 1.

Short answer

The answer is$232W$

Step-by-step solution

Description of the provided information 

Power $P=e\delta A{T}^4$

In this case

$\delta =5.67·{10}^{-8}$

$\frac{W}{m^2{K}^4}$is Stefan Boltzmann's constant

Result 

It can be stated that, temperature can be increased only to the melting point of lead and that is $T=328°C=601k$

The area of sphere:

$A={\mathrm{\pi D}}^2$

On the basis of maximum radiated power and substituting the values of numerics:
$P=1·5.67·{10}^{-8}·\mathrm{\pi }·0.1^2·{601}^4=232\mathrm{W}$

Therefore, the answer is 232w.