Concept explainers
Radiation Energy The total radiation energy E emitted by a heated surface per unit area varies as the fourth power of its absolute temperature T. The temperature is 6000 K at the surface of the sun and 300 K at the surface of the earth.
- (a) How many times more radiation energy per unit area is produced by the sun than by the earth?
- (b) The radius of the earth is 3960 mi, and the radius of the sun is 435,000 mi. How many times more total radiation does the sun emit than the earth?
(a)
To find: The number of times more radiation energy per unit area emitted by the sun than the earth.
Answer to Problem 43E
The radiation energy per unit area emitted by sun is greater than earth by factor of
Explanation of Solution
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 find: The number of times more total radiation emitted by the sun than the earth.
Answer to Problem 43E
The total radiation energy emitted by the sun is greater than the earth by the factor of
Explanation of Solution
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
Chapter 1 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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