Answer
(a) The power radiated by the sphere is 71 W
(b) The net flow rate of energy out of the sphere is 25 W
Work Step by Step
(a) We can find the power emitted by the sphere as:
$P = \epsilon \sigma A~T^4$
$P = \epsilon \sigma (4\pi~R^2)~T^4$
$P = (0.35)(5.67\times 10^{-8}~W/m^2~K^4)(4\pi)(0.19~m)^2(298~K)^4$
$P = 71~W$
The power radiated by the sphere is 71 W.
(b) We can find the net flow rate of energy out of the sphere as:
$\frac{Q}{t} = \epsilon \sigma A~(T_1^4-T_2^4)$
$\frac{Q}{t} = \epsilon \sigma (4\pi~R^2)~(T_1^4-T_2^4)$
$\frac{Q}{t} = (0.35)(5.67\times 10^{-8}~W/m^2~K^4)(4\pi)(0.19~m)^2~[(298~K)^4-(268~K)^4]$
$\frac{Q}{t} = 25~W$
The net flow rate of energy out of the sphere is 25 W.
