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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.11, Problem 43E

**(a)**

To determine

**To find:** The number of times more radiation energy per unit area emitted by the sun than the earth.

Expert Solution

The radiation energy per unit area emitted by sun is greater than earth by factor of

**Given:**

The total energy per unit area emitted by a heated surface is directly proportional to fourth power of its absolute temperature.

Temperature of surface of the sun is

Temperature of the surface of the earth is

**Calculation:**

The total radiation energy

That is,

Here,

To calculate Radiation energy

To calculate Radiation energy

Divide equation (2) by equation (3).

From the above equation,

Thus, the radiation energy emitted per unit surface area is greater than earth by factor of

**(b)**

To determine

**To find:** The number of times more total radiation emitted by the sun than the earth.

Expert Solution

The total radiation energy emitted by the sun is greater than the earth by the factor of

**Given:**

Radius

Radius

Temperature of surface of the sun is

Temperature of the surface of the earth is

**Calculation:**

Consider both earth and the sun as sphere.

Surface area of the sphere is

Here,

Use equation (1) and calculate total radiation energy emitted by the sun.

Substitute

Now, use equation (1) and calculate total radiation energy emitted by the earth

Substitute

Divide equation (4) by equation (5) and simplify.

Now, substitute

Thus, the total energy emitted by the sun is greater than the earth by the factor of approximately