Chapter 20, Problem 61A

A mercury barometer reads 760 mm at sea level. When it is carried to an altitude of 5.6 km, the height of the mercury column is reduced to half its initial value, or 380 mm.

a. What is the air pressure at this altitude relative to sea-level pressure?

b. If the barometer is taken up another 5.6 km to an altitude of 11.2 km, will the height of its mercury column fall another 380 mm and be zero? Why or why not?

To determine

The air pressure at an altitude relative to sea level pressure.

Answer to Problem 61A

The air pressure at an altitude relative to sea level pressure is half of its initial value of the column.

Explanation of Solution

Given:

The height of the mercury column is $h_{\text{mercury}}=\frac{h}{2}$ .

Formula used:

The expression for pressure is,

  $P=\rho gh$

Here, $\rho$ is the density, $g$ is the acceleration due to gravity, and $h$ is the height.

Calculation:

The air pressure at an altitude relative to sea level pressure is,

  $\begin{array}{l}P=\rho gh\\ P=\rho g{h}_{\text{mercury}}\\ P=\frac{\rho gh}{2}\end{array}$

Conclusion:

Thus, the air pressure at an altitude relative to sea level pressure is half of its initial value of the column.

To determine

To identify: Whether the height of its mercury column will fall another 380 mm and be zero for the given specifications.

Answer to Problem 61A

The height of its mercury column will be slightly decreased and should not be zero.

Explanation of Solution

Introduction:

Barometer is an instrument used for measuring the pressure of the atmosphere.

The mercury column’s vertical height remains constant even when the tube is tilted.

The mercury’s height in the barometer’s tube is used in measuring the atmospheric pressure.

The air pressure should not linearly vary with an altitude.

At an altitude of 11.2 km the height of its mercury column should not be zero.

The height of its mercury column will be decreased at an altitude of $11.2\text{ km}$ when compared to the altitude of $5.6\text{ km}$ .

Conclusion:

Thus, the height of its mercury column will be slightly decreased and should not be zero.