Pressure and Gases

In general, pressure is defined as the force exerted on a given area:

$\mathit{P}=\frac{\mathit{F}}{\mathit{A}}$

Note that pressure is directly proportional to force and inversely proportional to area. Thus, pressure can be increased either by increasing the amount of force or by decreasing the area over which it is applied; pressure can be decreased by decreasing the force or increasing the area.

The following table provides some information on these and a few other common units for pressure measurements

We can measure atmospheric pressure, the force exerted by the atmosphere on the earth’s surface, with a barometer (Figure below). A barometer is a glass tube that is closed at one end, filled with a nonvolatile liquid such as mercury, and then inverted and immersed in a container of that liquid. The atmosphere exerts pressure on the liquid outside the tube, the column of liquid exerts pressure inside the tube, and the pressure at the liquid surface is the same inside and outside the tube. The height of the liquid in the tube is therefore proportional to the pressure exerted by the atmosphere.

If the liquid is water, normal atmospheric pressure will support a column of water over $10$ meters high, which is rather inconvenient for making (and reading) a barometer. Because mercury ($\mathit{Hg}$) is about $13.6$-times denser than water, a mercury barometer only needs to be $\frac{1}{13.6}$ as tall as a water barometer—a more suitable size. The standard atmospheric pressure of 1 atm at sea level ($101325\mathit{Pa}$) corresponds to a column of mercury that is about $760\mathit{mm}$ ($29.92$ in.) high. The $\mathit{torr}$ was originally intended to be a unit equal to one millimeter of mercury, but it no longer corresponds exactly. The pressure exerted by a fluid due to gravity is known as hydrostatic pressure, $\mathit{p}$:

$\mathit{p}=\mathit{h\rho g}$

where $\mathit{h}$ is the height of the fluid, $\mathit{\rho }$ (lowercase Greek letter rho) is the density of the fluid, and $\mathit{g}$ is acceleration due to gravity.

Activity:

Try out the following application to understand how barometer is used to measure the atmospheric pressure.