Example

Question:

The density of the atmosphere at sea level is \(1.29\,\mathrm{kg\,m}^{-3}\). Assume that it does not change with altitude. Then how high would the atmosphere extend?

Solution:

We use Eq. (9.7): \[ \rho g h = 1.29\,\mathrm{kg\,m}^{-3} \times 9.8\,\mathrm{m\,s}^{-2} \times h = 1.01 \times 10^5\,\mathrm{Pa} \] \[ \Rightarrow h = \frac{1.01 \times 10^5}{1.29 \times 9.8} = 7989\,\mathrm{m} \approx 8\,\mathrm{km} \]
In reality, the density of air decreases with height, as does the value of \(g\). The atmospheric cover extends with decreasing pressure over 100 km. Note: the sea level atmospheric pressure is not always 760 mm of Hg; a drop in Hg level by 10 mm or more may indicate an approaching storm.