Answer
(a) The power radiated by the sun is $3.2\times 10^{26}~W$
(b) $I = 1100~W/m^2$
Work Step by Step
(a) We can find the power emitted by the sun as:
$P = \epsilon \sigma A~T^4$
$P = \epsilon \sigma (4\pi~R^2)~T^4$
$P = (1)(5.67\times 10^{-8}~W/m^2~K^4)(4\pi)(7.0\times 10^8~m)^2(5500~K)^4$
$P = 3.2\times 10^{26}~W$
The power radiated by the sun is $3.2\times 10^{26}~W$.
(b) We can find the power per unit area arriving at the earth as:
$I = \frac{P}{A}$
$I = \frac{P}{4\pi~r^2}$
$I = \frac{3.2\times 10^{26}~W}{(4\pi)(1.5\times 10^{11}~m)^2}$
$I = 1100~W/m^2$
