The solar energy coming to the earth by radiation is 1,340 W/m².If the sun has a radius of 7.000 $\times$ 10⁸m,is a perfect radiator and is located 1.500 $\times$ 10¹¹m from the earth,then what is the temperature of the sun?

Question

Quizplus · Accepted Answer

We can use the Stefan-Boltzmann law to relate the solar flux to the temperature of the sun:

Solar flux = σ × T^4 × (Sun's surface area) × (distance from the sun)^-2

where σ is the Stefan-Boltzmann constant.

The sun's surface area can be found using the formula for the surface area of a sphere:

Sun's surface area = 4π × (Sun's radius)^2

Plugging in the given values, we get:

1340 = σ × T^4 × 4π × (7 × 10^8)^2 × (1.5 × 10^11)^-2

Solving for T, we get:

T^4 = (1340 / (σ × 4π)) × ((1.5 × 10^11) / (7 × 10^8))^2

T^4 ≈ 1.74 × 10^14

Taking the fourth root of both sides, we get:

T ≈ 5760 K

Therefore, the answer is B.

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