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, ρ = ρ₀ exp(-z/z₀), where z is the height above sea level, ρ₀ is the density at sea level (you can use the Table 14.1 value), and z₀ is called the scale height of the atmosphere.

Table 14.1

Substance…………..ρ(kg/m³)

Helium gas…………...…...…..0.18

Air …………………………………1.29

Gasoline ………………….…….680

Ethyl alcohol ………....……..790

Benzene ……………………….880

Oil (typical) ………………...….900

Water …………………….…..1000

Seawater ……………….…...1030

Glycerin ………………….....1260

Mercury ………………......13,600

a. Determine the value of z₀.
b. What is the density of the air in Denver, at an elevation of 1600 m? What percent of sea-level density is this?