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

a.
`3.95*10^(26)`W

Step-by-step 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*10^(8))^(2)\\A = 6.2*10^(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*10^(-8)) (1) (6.2*10^(18)) (5800)^(4)\\P = 3.95*10^(26) W`