The surface of the Sun has a temperature of about 5800 K. If the radius of the Sun is 7*10⁸ m, determine the power output of the sun. (Take e = 1, and $\sigma$ = 5.67 *10^-⁸ W/m²·K⁴). A) 3.95 * 10²⁶ W B) 5.17 * 10²⁷ W C) 9.62 * 10²⁸ W D) 6.96 * 10³⁰ W

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The power output of the sun is given by the Stefan-Boltzmann law:$$P = \sigma A T^4$$where:* P is the power output in watts* σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2 K^4)* A is the surface area of the sun in square meters* T is the surface temperature of the sun in KelvinThe surface area of the sun is:$$A = 4\pi r^2$$where:* r is the radius of the sun in metersSubstituting the given values into the equations, we get:$$P = (5.67 x 10^-8 W/m^2 K^4) (4\pi (7 x 10^8 m)^2) (5800 K)^4$$$$P = 3.95 x 10^26 W$$Therefore, the power output of the sun is 3.95 x 10^26 W.

The Surface of the Sun Has a Temperature of About σ\sigmaσ

The Surface of the Sun Has a Temperature of About $\sigma$