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Physics Lesson 9.4.2 - Air (Atmospheric) Pressure

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Welcome to our Physics lesson on Air (Atmospheric) Pressure, this is the second lesson of our suite of physics lessons covering the topic of Gas Pressure, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Air (Atmospheric) Pressure

The first scientist who was successful in his attempts to measure the air pressure was Evangelista Torricelli, an Italian physicist and mathematician and a student of Galileo Galilei. He invented an air pressure gauge called "mercury barometer" or simply "barometer" which consists of an open vessel with a closed vertical tube at it middle as shown in the figure.

Physics Tutorials: This image provides visual information for the physics tutorial Gas Pressure

When the vessel is filled with mercury, its level is the same everywhere, even inside the tube (figure a), as this setup is a communicating vessel, as discussed in the previous tutorial "Liquid Pressure. Pascal's Principle ." This is because air exerts the same pressure on all parts of mercury surface.

If we remove the air from the upper part of the tube, mercury will start to raise up inside the tube, as there is no air above to hamper it from raising up. In this case, mercury acts as a capillary liquid, i.e. as a liquid that rises up in narrow tubes because of the change in pressure. This raise will continue until the liquid pressure caused by the mercury column will balance the air pressure aside (figure b). Therefore, since it is easy to measure the height h of mercury column and given that density of mercury is known (it is 13 600 kg/m3 or 13.6 g/cm3), we can calculate the air (atmospheric) pressure by working out the pressure of mercury column, i.e.

Pair = Pmercury column
= ρmercury × g × hmercury column

In normal atmospheric conditions (at sea level, in a sunny day at 150C), the mercury inside the column rises at 760 mm (76.0 cm or 0.760 m) above the neighbouring parts in contact with air. As a result, the atmospheric pressure in normal conditions is

Pair = 13 600 kg/m3 × 9.81 m/s2 × 0.760 m
≈ 101 325 Pa

Thus, we can write:

76 cm - Hg = 101 325 Pa

(Hg is the chemical symbol of mercury)

The above value can also be written as 1 atm (atmosphere). Thus, we have:

1 atm = 76 cm - Hg = 101 325 Pa

To facilitate calculations, another unit known as "bar" is often used. The conversion factor between bar and Pa is

1 bar = 100 000 Pa

Thus, we can say bar is slightly smaller than atm, as

1 bar = 100000/101325 atm = 0.9869 atm

On the other hand,

1 atm = 101325/100000
= 1.01325 bar
= 1013.25 mb

(mb means millibar)

High atmospheric pressure means the barometer shows values greater than 76 cm - Hg. Such a condition corresponds to cloudy skies and precipitations, as air charged with moisture is concentrated in the lower part of the sky. This increases the value of air pressure because an extra factor (moisture, i.e. water droplets) adds to the normal air pressure, giving a higher value in the barometer. On the other hand, low atmospheric pressure is associated with clear skies because the level of moisture in the air is very low.

Example 1

The barometer in a weather station shows 74 cm - Hg.

  1. What kind of weather is at the weather station location?
  2. What is the value of atmospheric pressure in Pa and millibar (mb)?

Solution 1

  1. The value shown by the barometer (74 cm - Hg) is smaller than the value of normal atmospheric pressure (76 cm - Hg). This means there is a good weather (clear sky) in the given location.
  2. We use the cross-production rule to convert the value in the desired units. Thus,
76 cm - Hg = 101 325 Pa
74 cm - Hg = x Pa

We have

x = 101 325 × 74/76
= 98 659 Pa

The same procedure is used to convert the atmospheric pressure from Pa to millibar. Thus,

100 000 Pa = 1 bar
98 659 Pa = x bar

We have

x = 98 659 × 1/100 000 = 0.98659 bar
= 986.59 mb

You have reached the end of Physics lesson 9.4.2 Air (Atmospheric) Pressure. There are 6 lessons in this physics tutorial covering Gas Pressure, you can access all the lessons from this tutorial below.

More Gas Pressure Lessons and Learning Resources

Density and Pressure Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
9.4Gas Pressure
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
9.4.1Air as a Mixture of Gases
9.4.2Air (Atmospheric) Pressure
9.4.3Why is Mercury Used as Capillary Liquid in Barometers?
9.4.4Gas Pressure
9.4.5Total Pressure in Water
9.4.6How does the Atmospheric Pressure Vary with Altitude?

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