The Existence of Atmospheric Pressure, Its Units and What Changes It – Atmospheric Pressure and Archimedes' Principle (Senior 3 Physics) | Ganzaa

Atmospheric Pressure and Archimedes' Principle

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Senior 3 · Physics

Atmospheric Pressure and Archimedes' Principle

5 lessons

Lesson 1 of 5

The Existence of Atmospheric Pressure, Its Units and What Changes It

25 min

The swollen packet

A hiker buys a sealed packet of biscuits in Musanze and carries it up Mount Karisimbi. Near the summit, the packet is swollen tight like a balloon, although nothing has been added to it. On the way back down it goes slack again.

The air sealed inside the packet has not changed. What has changed is the air outside. At the bottom of the mountain there is far more air above the hiker than at the top, and its weight presses on the packet from every side. In S2 you measured this pressure with a mercury barometer. In this lesson you will see the evidence that it exists, express it in its different units, and find out what makes it rise and fall.

Evidence for atmospheric pressure

The collapsing can. A little water is boiled in a thin metal can with its cap off. The steam drives most of the air out. The can is taken off the heat, the cap is screwed on at once, and cold water is poured over it. Within seconds the can crumples with a bang.

Cooling makes the steam inside condense back to a few drops of water, leaving almost nothing inside to push outwards. The air outside still presses on every square centimetre of the can, and the thin metal cannot resist it. Nothing "sucked" the can in: it was pushed in by the atmosphere.

The card and the glass. Fill a glass to the brim with water, slide a stiff card over the top, hold the card and turn the glass upside down, then let go of the card. The card stays in place and the water stays in the glass: the air pressing up on the card is far greater than the pressure of the water pressing down. Atmospheric pressure acts in every direction, not only downwards.

The Magdeburg hemispheres. In the 1650s the German scientist Otto von Guericke fitted two metal hemispheres together and pumped the air out from between them. Teams of horses pulling in opposite directions could not separate them; when air was let back in, they fell apart by hand.

Important

Safety for the collapsing can. This is a teacher demonstration. Use only a few centimetres of water, hold the can with tongs or heat-proof gloves, and put the cap on only after taking the can off the heat: a sealed can that is still being heated can burst. Keep faces away from the steam.

Definition

Atmospheric pressure: the pressure exerted by the weight of the air above a surface, acting equally in all directions at a given point. At sea level it is about $1.01 \times 10^{5}\ \text{Pa}$ .

Pascal (Pa): the SI unit of pressure, $1\ \text{Pa} = 1\ \mathrm{N\,m^{-2}}$ . Standard atmospheric pressure (1 atm) is defined as 101 325 Pa, the pressure that holds up 760 mm of mercury.

Units of atmospheric pressure

Unit	Value of 1 unit	Where you meet it
pascal (Pa), kilopascal (kPa)	1 kPa = 1000 Pa	Science, engineering
hectopascal (hPa) = millibar (mbar)	100 Pa	Weather maps and forecasts
bar	$1 \times 10^{5}$ Pa	Tyre gauges, gas cylinders
standard atmosphere (atm)	101 325 Pa	Chemistry, diving
millimetre of mercury (mmHg)	about 133 Pa	Barometers, blood pressure

Worked example 1: converting units

A barometer in Kigali reads 84 kPa. Express this in hPa, in bar and in atmospheres.

84\ \text{kPa} = 84\,000\ \text{Pa} = \frac{84\,000}{100} = 840\ \text{hPa}

\frac{84\,000}{1 \times 10^{5}} = 0.84\ \text{bar} \qquad \frac{84\,000}{101\,325} \approx 0.83\ \text{atm}

Worked example 2: the force of the air on a desk

A desk top measures 1.2 m by 0.60 m. Find the force of the air pressing down on it in Kigali, where the atmospheric pressure is 84 kPa. Why does the desk not collapse?

F = p\,A = 84\,000 \times (1.2 \times 0.60) = 84\,000 \times 0.72 \approx 60\,000\ \text{N}

That is about the weight of six tonnes. The desk survives because the air also presses upwards on the underside of the desk top with an almost equal force, so the resultant force from the air is nearly zero.

What changes atmospheric pressure?

Altitude. The higher you go, the less air there is above you, so the pressure falls. The air is also compressed by its own weight, so it is densest near the ground and thins out with height: the pressure therefore does not fall at a steady rate. The table uses the International Standard Atmosphere, a model that engineers and pilots use for average conditions.

Place	Height above sea level	Atmospheric pressure (model)	Mercury barometer
Sea level	0 m	101 kPa	760 mm
Lake Kivu	about 1,460 m	85 kPa	about 637 mm
Kigali (average)	about 1,570 m	84 kPa	about 629 mm
Summit of Karisimbi, Rwanda's highest point	4,507 m	58 kPa	about 432 mm
Airliner at cruising height	about 11,000 m	23 kPa	about 170 mm

At the top of Karisimbi each breath holds only about 57% as much air as at sea level, which is why climbers get breathless so quickly. Your ears "pop" on a fast drive down from Musanze to Kigali, as the air pressure outside your eardrum changes before the pressure inside can match it.

Worked example 3: from valley to ridge

Kigali's valleys lie at about 1,300 m and its ridges at about 1,600 m. Taking the density of air there as $1.05\ \mathrm{kg\,m^{-3}}$ and $g = 9.8\ \mathrm{N\,kg^{-1}}$ , estimate how much lower the pressure is on a ridge than in a valley.

Over a small height the air's density hardly changes, so the liquid-pressure rule from S2 can be used for the air column:

\Delta p = \Delta h\,\rho\,g = 300 \times 1.05 \times 9.8 \approx 3100\ \text{Pa} = 3.1\ \text{kPa}

Near the ground, pressure falls by roughly 1 kPa for every 100 m you climb. (For large heights this rule fails, because the air grows thinner as you go up.)

Temperature, humidity and weather

Temperature. Warm air expands and becomes less dense, so a column of warm air presses down less. Regions of rising warm air are regions of low pressure.
Humidity. A water molecule (relative mass 18) is lighter than the nitrogen and oxygen molecules (28 and 32) it replaces, so moist air is less dense than dry air and exerts slightly less pressure.
Weather. Day-to-day pressure changes are small, a few hPa, but they matter. A falling barometer usually means warm, moist, rising air and a chance of cloud and rain; a rising barometer usually means settled weather.

Warning

Air does not "suck". A can collapses, a sucker sticks and a straw works because the air on one side pushes harder than whatever is on the other side. Always explain these effects with a pressure difference and the direction of the push.

Tip

Numbers to remember: sea level 101 kPa = 1013 hPa = 760 mmHg; Kigali about 84 kPa; near the ground, about 1 kPa less for every 100 m of height.

Crush a steel drum with air pressure (Imagination Station, Toledo). The collapsing can on a giant scale: watch the sealed, steam-filled drum as it cools and the steam inside condenses.

✦

Practice

Describe one experiment that shows that the atmosphere exerts a pressure. Explain what happens.
Convert 84 kPa into (a) hPa; (b) bar; (c) atmospheres.
A window measures 1.5 m by 1.0 m. Find the force of the air on one side of it in Kigali (84 kPa). Why does the window not break?
Explain why the atmospheric pressure at the summit of Karisimbi is lower than in Kigali.
Estimate the difference in air pressure between the bottom and the top of a 50 m tall building in Kigali ( $\rho_{air} = 1.05\ \mathrm{kg\,m^{-3}}$ , $g = 9.8\ \mathrm{N\,kg^{-1}}$ ).
A packet of biscuits sealed in Kigali (84 kPa) is carried to a place where the pressure is 58 kPa. What happens to the packet, and why?
Why can a falling barometer reading be a sign that rain is coming?
A pupil says: "Air pressure is caused by the weight of the air, so it can only push downwards." Use the card-and-glass experiment to show that this is wrong.

Show answersHide answers

For example, the collapsing can: a little water is boiled in a can, the cap is put on and the can is cooled. The steam condenses, so the pressure inside becomes very low, and the greater atmospheric pressure outside crushes the can.
(a) 840 hPa; (b) 0.84 bar; (c) $\frac{84\,000}{101\,325} \approx 0.83$ atm.
$F = pA = 84\,000 \times 1.5 = 126\,000\ \text{N}$ . The air inside the room presses on the other side with an equal pressure, so the forces balance.
At the summit there is much less air above, so the weight of the air column pressing on each square metre is smaller; the air up there is also thinner (less dense).
$\Delta p = 50 \times 1.05 \times 9.8 \approx 510\ \text{Pa}$ (about 0.5 kPa).
It swells. The air sealed inside is still at about 84 kPa, but the air outside now presses with only 58 kPa, so the inside pushes the packet outwards.
A falling pressure often means warm, moist air rising overhead. Moist, warm air is less dense, and as it rises it cools and its water vapour condenses into clouds and rain.
In the card-and-glass experiment the card is held up against the weight of the water by the air pressing upwards on it. So the air pushes upwards (and sideways) as well as down: at any point, fluid pressure acts equally in all directions.

Key points

The weight of the air above us causes atmospheric pressure, which acts in all directions: shown by the collapsing can, the card and glass, and the Magdeburg hemispheres.
Units: Pa ( $\mathrm{N\,m^{-2}}$ ), hPa (weather), bar, atm and mmHg; 1 atm = 101 325 Pa = 760 mmHg.
Pressure falls with altitude: about 84 kPa in Kigali and 58 kPa on Karisimbi's summit.
Warm, moist air is less dense and gives lower pressure; a falling barometer often means rain.

Sources and credits

Chapter 11: Fluid Statics, from College Physics (1st edition) by Paul Peter Urone and Roger Hinrichs, OpenStax, hosted by LibreTexts, licensed under CC BY 4.0. Consulted for the physics; no text was copied.
Heights: Kigali's average elevation (1,567 m) and its valleys (about 1,300 m) from Kigali: State of Environment and Outlook Report 2013, Rwanda Environment Management Authority (REMA), p. 7; Karisimbi (4,507 m) from Mount Karisimbi, Encyclopaedia Britannica; Lake Kivu (about 1,460 m) from Lake Kivu, Encyclopaedia Britannica. Pressures were calculated by Ganzaa from the International Standard Atmosphere, so real readings vary with the weather.
Image: Pranishnikoff Flammarion Experience des hemispheres de Magdeburg.jpg by Ivan Pranishnikoff (1888), public domain, via Wikimedia Commons.
Photo: Karisimbi.jpg by SIBOMANA Constantin, Wikimedia Commons, licensed under CC BY-SA 4.0.
Video: Crush a steel drum with air pressure, Imagination Station Toledo, embedded from YouTube.

Written by Ganzaa: the lesson text, the collapsing-can diagram, the tables, worked examples and practice exercises.

1The swollen packet

2Evidence for atmospheric pressure

3Units of atmospheric pressure

4What changes atmospheric pressure?

5Temperature, humidity and weather

The swollen packet

Evidence for atmospheric pressure

Units of atmospheric pressure

What changes atmospheric pressure?

Temperature, humidity and weather