Question

The Sun is a sphere with a radius of approximately 6.96 x 10^8 m and a surface temperature of 5778 K. The emissivity at the surface is ε = 1.0, and σ = 5.67 x 10-8 W/m^2∙K^4. Calculate the rate at which the Sun is radiating energy into space in Watts.​

Answer 1

Answer:

Although much hotter on the inside, we can closely approximate the surface of the sun, from which its emission occurs, as a black body at a temperature of about 5800 K. The Stefan-Boltzmann equation then gives the energy flux emitted at the sun’s surface.

SS = (5.67 × 10–8 W·m–2·K–4)(5800 K)4 = 63 × 106 W·m–2

The surface area of a sphere with a radius r is 4πr2. If rS is the radius of the Sun, the total energy it emits is SS4πrs2. As the radiation is emitted from this spherical surface, it is spread over larger and larger spherical surfaces, so the energy per square meter decreases, as illustrated schematically in the diagram below.

Explanation:

here is your correct answer

Answer 2

Answer:

According to Stefan Law Of Radiation, we can state:

P = σεAT⁴

Since ε = 1

P = σAT⁴

Now Area A = 4πr² ≈ 6.087 × 10¹⁸ m²

So Rate at which sun radiates energy = Power

= 5.67 × 10⁻⁸ × 6.087 × 10¹⁸ × (5778)⁴

= 3.846 × 10²⁶ W

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