Question

The surface of the Sun has a temperature of about 5 800 K. If the radius of the Sun is 7 × 108 m, determine the power output of the sun. (Take e = 1, and σ = 5.67 × 10−8W/m2⋅K4).
a. 3.95 × 1026 W
b. 5.17 × 1027 W
c. 9.62 × 1028 W
d. 6.96 × 1030 W

Answer 1

Answer:

a. $3.95\times10^{26}$W

Explanation:

$T$ = temperature of the surface of sun = 5800 K

$r$ = Radius of the Sun = 7 x 10⁸ m

$A$ = Surface area of the Sun

Surface area of the sun is given as

$A = 4\pi r^{2} \\A = 4(3.14) (7\times10^{8})^{2}\\A = 6.2\times10^{18} m^{2}$

$e$ = Emissivity = 1

$\sigma$ = Stefan's constant = 5.67 x 10⁻⁸ Wm⁻²K⁻⁴

Using Stefan's law, Power output of the sun is given as

$P = \sigma e AT^{4} \\P = (5.67\times10^{-8}) (1) (6.2\times10^{18}) (5800)^{4}\\P = 3.95\times10^{26} W$