Modern Physics

Torricelli experiment: atmospheric pressure measurements, importance

The Torricelli experiment was conducted by the Italian physicist and mathematician Evangelista Torricelli in 1644 and in the first measurement of atmospheric pressure.

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

the experiment

In 1644, Torricelli carried out the following experiment:

– Introduced mercury into a 1 m long tube, open at one end and closed at the other.

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

– Torricelli noticed that the column descended and stopped about 76 cm high.

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

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

Then the mercury descended and the water rose. The vacuum obtained, as we said, was not perfect, because there were always traces of mercury vapor or water.

Atmospheric pressure measurement

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 pull exerted by the Earth is responsible for maintaining the whole around the planet.

Obviously, the composition is not uniform, nor the density, as it depends on the temperature. Near the surface, there is a fair amount of dust, sand and pollutants from natural events as well as human activity. The heavier molecules are closer to the ground.

As there is a lot of variability, it is necessary to choose a reference altitude for the atmospheric pressure, which it is convenient to consider the sea level.

It’s not about any sea level, because it also has fluctuations. the level or data is chosen with the help of a geodetic reference system established in agreement among the experts.

How much is the atmospheric pressure near the ground? Torricelli found his value by measuring the height of the column: 760 mm of mercury.

The Torricelli Barometer

At the top of the tube, the pressure is 0, as a vacuum has been established there. While on the surface of the mercury bath pressure 1 is atmospheric pressure.

Let’s choose the origin of the reference system from the mercury-free surface at the top of the tube. From there, until reaching the surface of the mercury in the container, H , the height of the column, is measured.

The pressure at the point marked with red, at depth and 1 is:

1 = P or + ρ Hg . ge 1

Where ρ Hg is the density of mercury. As 1 = H and Po = 0 :

1 = ρ Hg . g .H

H = P 1 / ρ Hg .g

The mercury density is constant and gravity is constant, it appears that the height of the mercury column is proportional to 1 , which is atmospheric pressure. Replacing known values:

H = 760 mm = 760 x 10 -3 m

g = 9.8 m / s 2

ρ Hg = 13.6 g / cc = 13.6 x 10 3 kg / m 3

1 = 13.6 x 10 3 kg / m 3 x 9.8 m / s 2 x 760 x 10 -3 m = 101,293 N / m 2 = 101.3 kN / m 2

The unit of pressure in the International System is the Pascal, abbreviated to Pa. According to Torricelli’s experiment, the atmospheric pressure is 101.3 kPa.

Importance of atmospheric pressure to climate

Torricelli observed that the level of mercury in the tube underwent small changes every day, and deduced that the atmospheric pressure must change as well.

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Atmospheric pressure is responsible for much of the climate, but its daily variations go unnoticed. It’s because they’re not as remarkable as storms or cold weather, 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 decrease.

When the barometer indicates high pressures, you can expect a good amount of time, while at low pressures, there is the possibility of storms. However, to make accurate weather forecasts, more information about other factors is needed.

The torr and other pressure units

Although it seems 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.

That’s because the mercury barometer is still used today with little variation since that time, so in honor of Torricelli, 760 mm of Hg equals 1 torr. In other words:

1 torr = 760 mm Hg = 30 inches of Hg = 1 atmosphere of pressure = 101.3 kPa

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

Other extended use units are bars and millibars. One millibar is equivalent to one hectopascal or 10 2 pascals.

Altimeters

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

If the height is not too great, in principle we can assume that the air density remains constant. But this is an approximation, because we know that the density of the atmosphere decreases with height.

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

1 = P or + ρ ar . gH

In this expression, a is the atmospheric pressure Considered at the ground level and P 1 is que Whose place of the elevation is determined to be:

H = (P 1 – P o ) / ρ ar . g

Torricelli experiment: atmospheric pressure measurements, importance 3

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

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