Chapter 18, Problem 1GST

To determine

The height of the barometer that is required to measure the standard sea level pressure if the barometer is built using mercury.

Answer to Problem 1GST

The height of the required barometer is 403.65 inches.

Explanation of Solution

Given info:

The density of the mercury is 13.5 times heavier than water.

Density is given as the ratio of the mass to the volume and the volume is the product of area and height.

Express the relation for density.

$\text{Density}=\frac{\text{mass}}{\text{area}\times \text{height}}$

Hence, the density is inversely proportional to the height $\left(\text{Density}\propto \text{Height}\right)$.

The average sea-level pressure in the normal mercury barometer is recorded at 29.94 inches on the mercury barometer.

The expression for calculating the height of barometer with water is as follows:

$\text{Height of water barometer}=\frac{\text{Density of mercury}}{\text{Density of water}}\times \{\begin{array}{l}\text{height shown on mecury barometer }\\ \text{to record average sea level pressure}\end{array}$

Substitute $13.5\text{g}/{\text{cm}}^{\text{3}}$ for density of mercury, $1\text{g}/{\text{cm}}^{\text{3}}$ for density of water, and the height shown on the mercury barometer to record the average sea level pressure as 29.94 inches.

$\begin{array}{c}\text{Height of water barometer}=\frac{13.5\text{g}/{\text{cm}}^{\text{3}}}{1\text{g}/{\text{cm}}^{\text{3}}}\times 29.94\text{inches}\\ =403.65\text{inches}\end{array}$

Conclusion:

The height of the barometer that is required to measure the standard sea level pressure if the barometer is built using mercury is $403.65\text{inches}$