Chapter 10, Problem 15P

To determine

The height of atmosphere is to be found if its density is equal to half the present density at sea level.

Answer to Problem 15P

The height of atmosphere is $16876m\approx 16.876km$

Explanation of Solution

Given info:

Density at sea level, ${\rho }_a=1.225{\text{kg/m}}^{\text{3}}$

Density of air throughout, $\rho =\frac{1.225}{2}{\text{kg/m}}^{\text{3}}=0.6125{\text{kg/m}}^{\text{3}}$

Atmospheric pressure, $P=1atm=1.013\times {10}^{5}Pa$

Formula used:

Pressure is given by, $P=\rho gh$

Calculation:

Substituting values in formula of Pressure,

  $\begin{array}{l}1.013\times {10}^5=(0.6125)(9.8)h\\ h=\frac{1.013\times {10}^5}{(0.6125)(9.8)}\\ h=16876m\approx 16.876km\end{array}$

Conclusion:

The height of atmosphere is $16876m\approx 16.876km$