Atmospheric Pressure and Barometers
Atmospheric pressure is the pressure exerted by the weight of the air above a point, about 101,325 Pa (1 atmosphere) at sea level, and a barometer is an instrument that measures it, for example by the height of a mercury column, which is about 760 mm at sea level. In brief: atmospheric pressure decreases with altitude, because there is less air above. A mercury barometer balances the weight of the mercury column against the weight of the atmosphere: p = ρgh. An aneroid barometer uses a sealed flexible metal box that flexes with the pressure.
We do not feel the weight of the air, even though it presses on every square meter of our bodies with a force of about 100,000 N, because the fluids in our bodies push outward with the same pressure. This guide explains the origin of atmospheric pressure, how the barometers work, how pressure changes with altitude, compares units in a table, works through calculations and corrects common mistakes.
What causes atmospheric pressure?
Air has mass, so the column of air above the surface of the Earth has weight. The pressure is the weight of that column per unit area. It is also explained by the collisions of air molecules with surfaces. At sea level, the pressure is on average 101,325 Pa = 1013 hPa (millibars) = 1 atm = 760 mmHg. Everyday phenomena that depend on atmospheric pressure include drinking through a straw (the pressure inside the mouth is lowered, and the atmosphere pushes the liquid up), suction cups, and the difficulty of separating two joined flat surfaces with a vacuum between them.
How do barometers work?
- Mercury barometer: a glass tube about 1 m long, closed at one end, is filled with mercury and inverted into a dish of mercury. The mercury falls until the pressure of the column ρgh equals the atmospheric pressure on the dish, leaving a vacuum above (Torricellian vacuum). The height of the column, measured from the dish, is the pressure in mmHg. Its height does not depend on the width or slope of the tube.
- Aneroid barometer: contains a sealed, partly evacuated metal capsule with a flexible lid. Changes in air pressure make the lid move, and levers move a pointer. It is portable and is used in altimeters (aircraft, hikers) and weather stations.
- Electronic sensors in phones and weather stations measure the deformation of a membrane.
Mercury is used because its high density (13,600 kg/m3) gives a column of manageable height. A water barometer would need a tube more than 10 m tall.
How does the pressure change with altitude and weather?
With increasing altitude, the pressure decreases, rapidly at first: near sea level, it drops about 1 hPa for every 8 to 10 m of height, and at the top of Mount Everest (8,849 m) it is only about one-third of the sea-level value (about 31 to 34 kPa). Weather also changes the pressure by a few percent: low-pressure systems are associated with clouds and rain, and high pressure with clear, dry weather. The change is the basis of altimeters and of weather forecasting.
Units of pressure compared
| Unit | Value of 1 standard atmosphere |
|---|---|
| pascal (Pa) | 101,325 Pa |
| hectopascal (hPa) or millibar (mbar) | 1,013.25 |
| millimeters of mercury (mmHg) | 760 |
| bar | 1.01325 |
| pounds per square inch (psi) | 14.7 |
Worked example: barometer height and force of the air
- Height of mercury. h = p ÷ (ρg) = 101,325 ÷ (13,600 × 9.8) = 101,325 ÷ 133,280 = 0.760 m = 760 mm.
- Height of a water barometer. h = 101,325 ÷ (1,000 × 9.8) = 10.3 m.
- Force on a surface. A table top of area 1.2 m2: F = pA = 101,325 × 1.2 = 1.2 × 105 N. This is about 12 tonnes-force, but the air under the table pushes up with an equal force, so the table is not crushed.
- Pressure change on a hill. If the pressure drops by 1 hPa for every 9 m, then climbing 450 m reduces the pressure by 450 ÷ 9 = 50 hPa, from 1,013 hPa to about 963 hPa, a fall of 5 percent. The rule is approximate and holds only near sea level.
How was atmospheric pressure discovered?
Evangelista Torricelli made the first mercury barometer in 1643 and explained that the mercury is held up by the weight of the atmosphere. Blaise Pascal asked his brother-in-law to carry a barometer up the Puy de Dôme in 1648, and the mercury was lower at the top. Otto von Guericke’s Magdeburg hemispheres (1654) showed the force of air pressure: two teams of horses could not pull apart two copper hemispheres with the air pumped out.
Which mistakes are common?
Mistake 1: Thinking that air has no weight
Air has mass. A cubic meter of air at sea level has a mass of about 1.2 kg.
Mistake 2: Saying that a vacuum “sucks”
The higher outside pressure pushes. The vacuum does not pull.
Mistake 3: Using the length of the tube for the barometer reading
The pressure depends on the vertical height of the column above the level in the dish.
Mistake 4: Assuming that the pressure falls in a straight line with height
It falls exponentially, because the air becomes less dense as you go higher.