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Q.48

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 386

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Short Answer

It's possible to use the ideal-gas law to show that the density of the earth's atmosphere decreases exponentially with height. That is, , where is the height above sea level, is the density at sea level (you can use the Table value), and is called the scale height of the atmosphere.

a. Determine the value of .

Hint: What is the weight of a column of air?

b. What is the density of the air in Denver, at an elevation of ? What percent of sea-level density is this?

Hence the percentage is

See the step by step solution

Step by Step Solution

Step :1 Introduction (part a)

The density of the earth's atmosphere decreases exponentially with height. The expression for density can be started as

Where, is the height above the sea level, is the density at the sea level and is the scale height of the atmosphere.

Step :2 Explanation (parta)

Consider a small air column which extends from the sea level to the outer atmosphere. The cross sectional area of the column is .Take an element of thickness of the air column.Thus the volume of such an element is

The height of the element

Thus the total weight if the air column with area of is

Substitute

Hence the scale weight is

Step :3 Density variation(part b)

We have an expression for density variation with height as

Where is the height above the sea level is the density at sea level and is the scale height of the atmosphere

Step :4 Percentage of density (part b)

The density of air at sea level. Substitute

The percentage of density as compared to sea level density is

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