Assume that the sun is a sphere of radius 6.96 × 10⁸ m and that its surface temperature is 5.8 × 10³ K.If the sun radiates at a rate of 3.90 × 10²⁶ W and is a perfect emitter,at what rate is energy emitted per square meter at the sun's surface?
A)5.6 × 10⁷ W/m²
B)6.4 × 10⁷ W/m²
C)5.6 × 10¹⁷ W/m²
D)12.8 × 10⁷ W/m²
E)25.6 × 10⁷ W/m²

Question

Quizplus · Accepted Answer

The rate at which energy is emitted per square meter at the sun's surface (also known as the surface flux) can be calculated using the Stefan-Boltzmann law, which states that the energy radiated per unit time per unit area is proportional to the fourth power of the temperature and is given by:

j = σT⁴

where σ is the Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²K⁴).

Plugging in the given values, we get:

j = (5.67 × 10⁻⁸ W/m²K⁴)(5.8 × 10³ K)⁴
j = 6.39 × 10⁷ W/m²

Therefore, the rate at which energy is emitted per square meter at the sun's surface is 6.39 × 10⁷ W/m², which is closest to choice B (6.4 × 10⁷ W/m²).

Assume That the Sun Is a Sphere of Radius 6