   Chapter 11, Problem 71AP

Chapter
Section
Textbook Problem

The surface of the Sun has a temperature of about 5800 K. The radius of the Sun is 6.96 × 108 m. Calculate the total energy radiated by the Sun each second. Assume the emissivity of the Sun is 0.986.

To determine

The total energy radiated by the sun each second.

Explanation

Given Info: The surface temperature of the sun is 5800 K, the radius of the sun is 6.96×108m, and emissivity of the sun is 0.986.

Formula to calculate the net power radiatedby the sun is,

P=σAeT4

• P is power radiated from the sun,
• σ is Stefan-Boltzmann constant,
• e is the emissivity of the sun,
• T is the surface temperature of the sun,
• A is the surface area of the sun,

Formula to calculate the surface area of the sun is,

A=4πr2

• r is the radius of the sun,

Use 4πr2 for A in P=σAeT4 to rewrite P.

P=σ(4πr2)eT4

Formula to calculate the energy radiated by the sun each second is,

E=P.Δt

• E is the energy radiated by the sun each second
• Δt is the time.

Use σ(4πr2)eT4 for P in the above equation to rewrite it.

E=(σ(4πr2)eT4)Δt

Substitute 5

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