TORRICELLI EXPERIMENT: ATMOSPHERIC PRESSURE MEASUREMENTS, IMPORTANCE - PHYSICAL - 2025

The experiment Torricelli was carried out by physical and Italian mathematician Evangelista Torricelli in 1644 and resulted in the first measurement of the atmospheric pressure.

This experiment arose from the need to improve the water supply in cities. Evangelista Torricelli (1608-1647), who was a court mathematician to the Grand Duke of Tuscany Ferdinand II, had studied hydraulic phenomena together with Galileo.

Figure 1. Torricelli's experiment, in which the mercury column rises 760 mm due to atmospheric pressure. Source: F. Zapata.

The experiment

In 1644, Torricelli made the following experiment:

- He introduced mercury into a tube 1 m long, open at one end and closed at the other.

- When the tube was completely full, he inverted it and dumped it into a container that also contained mercury.

- Torricelli observed that the column descended and stopped at about 76 cm high.

- He also noticed that a vacuum had been generated in the space that was free, although not perfect.

Torricelli repeated the experiment using different tubes. He even made a small variation: he added water to the bucket, which, being lighter, floated on the mercury. Then he slowly raised the tube containing mercury to the surface of the water.

Then the mercury went down and the water went up. The vacuum obtained, as we have already said, was not perfect, because there were always remnants of mercury vapor or water.

The measurement of atmospheric pressure

The atmosphere is a mixture of gases in which nitrogen and oxygen predominate, with traces of other gases such as argon, carbon dioxide, hydrogen, methane, carbon monoxide, water vapor and ozone.

The gravitational attraction exerted by the Earth is responsible for keeping the whole surrounding the planet.

Of course, the composition is not uniform, and neither is the density, since it depends on the temperature. Near the surface there is a good amount of dust, sand and pollutants from natural events and also from human activity. The heavier molecules are closer to the ground.

Since there is so much variability, it is necessary to choose a reference altitude for atmospheric pressure, which for convenience has been taken as sea level.

Here it is not just any sea level, because that also presents fluctuations. The level or datum is chosen with the help of some geodetic reference system fixed by common agreement between the experts.

What is the atmospheric pressure near the ground worth? Torricelli found its value when he measured the height of the column: 760 mm of mercury.

The Torricelli barometer

At the top of the tube the pressure is 0, since a vacuum has been established there. Meanwhile, on the surface of the mercury vat, the pressure P ₁ is atmospheric pressure.

Let's choose the origin of the reference frame on the free surface of the mercury, at the top of the tube. From there to the surface of the mercury in the container, measure H, the height of the column.

Figure 2. The Torricelli barometer. Source: General Physics for Engineers. J. Lay. USACH.

The pressure at the point marked in red, at depth y ₁ is:

Where ρ _Hg is the density of mercury. Since y ₁ = H and Po = 0:

Since the density of mercury is constant and gravity is constant, it turns out that the height of the mercury column is proportional to P ₁ , which is the atmospheric pressure. Substituting known values:

The unit for pressure in the International System is the pascal, abbreviated Pa. According to Torricelli's experiment, atmospheric pressure is 101.3 kPa.

Importance of atmospheric pressure for the climate

Torricelli observed that the level of mercury in the tube underwent slight variations every day, so he deduced that the atmospheric pressure must also change.

Atmospheric pressure is responsible for much of the climate, however its daily variations go unnoticed. It is because they are not as noticeable as storms or cold, for example.

However, these variations in atmospheric pressure are responsible for the winds, which in turn influence rainfall, temperature and relative humidity. When the ground heats up, the air expands and tends to rise, causing the pressure to drop.

Whenever the barometer indicates high pressures, good weather can be expected, while with low pressures there is the possibility of storms. However, to make accurate weather predictions, you need more information about other factors.

He

Although it sounds strange, since pressure is defined as force per unit area, in meteorology it is valid to express atmospheric pressure in millimeters of mercury, as established by Torricelli.

This is because the mercury barometer continues to be used today with little variation since that time, so that in honor of Torricelli, 760 mm of Hg is equal to 1 torr. In other words:

If Torricelli had used water instead of mercury, the height of the column would be 10.3 m. The mercury barometer is more practical as it is more compact.

Other units in widespread use are bars and millibars. One millibar is equal to one hectopascal or 10 ² pascals.

Altimeters

An altimeter is an instrument that indicates the height of a place, comparing the atmospheric pressure at that height with that on the ground or another reference place.

If the height is not very great, in principle we can assume that the density of the air remains constant. But this is an approximation, since we know that the density of the atmosphere does decrease with height.

Using the equation used above, the density of air is used instead of that of mercury:

In this expression P _o is taken as the atmospheric pressure at ground level and P1 is that of the place whose altitude is to be determined:

The altimetric equation shows that pressure decreases exponentially with height: for H = 0, P ₁ = P _or and if H → ∞, then P ₁ = 0.

References

1. Figueroa, D. 2005. Series: Physics for Sciences and Engineering. Volume 5. Fluids and Thermodynamics. Edited by Douglas Figueroa (USB).
2. Kirkpatrick, L. 2007. Physics: A Look at the World. 6th abridged edition. Cengage Learning.
3. Lay, J. 2004. General Physics for Engineers. USACH.
4. Mott, R. 2006. Fluid Mechanics. 4th. Edition. Pearson Education.
5. Strangeways, I. 2003. Measuring the Natural Environment. 2nd. Edition. Cambridge University Press.