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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

Respuesta :

Answer:

a. [tex]3.95\times10^{26} [/tex]W

Explanation:

[tex]T[/tex] = temperature of the surface of sun = 5800 K

[tex]r[/tex] = Radius of the Sun = 7 x 10⁸ m

[tex]A[/tex] = Surface area of the Sun

Surface area of the sun is given as

[tex]A = 4\pi r^{2} \\A = 4(3.14) (7\times10^{8})^{2}\\A = 6.2\times10^{18} m^{2}[/tex]

[tex]e[/tex] = Emissivity = 1

[tex]\sigma[/tex] = Stefan's constant = 5.67 x 10⁻⁸ Wm⁻²K⁻⁴

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

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

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