Barometer & Atmospheric Pressure

Atmospheric Pressure

Air is a fluid. We are living at the bottom of a “sea” of air called the atmosphere. The weight of the Earth’s atmosphere pushing down on each unit area of Earth’s surface constitutes the atmospheric pressure.

Origin of Atmospheric Pressure

Atmospheric pressure exists because of molecular bombardment by energetic air molecules. Under normal conditions, there is a large number of air molecules moving at high velocities. This large number of air molecules make frequent collisions with the walls of the container. When the air molecules hit the wall, they rebound from the wall and a force is exerted on the wall from the rebound. The force per unit area exerted by the air molecules on the wall is referred to as the air pressure on the wall. More information on this can be found in Three States of Matter and the subsequent sub-topics.

Atmospheric Pressure at Sea Level

The pressure exerted by this layer of air at sea level is $1.013 \times 10^{5} \, \text{Pa}$. This value is referred to as one atmosphere and is equivalent to placing 1 kg weight on an area of $1 \text{ cm}^{2}$. The pressure at higher altitudes is lower.

Barometer

A barometer is a simple instrument for measuring atmospheric pressure.

A barometer can be made by filling up a long glass tube with mercury, then turning it upside down in a bath of mercury as shown. The space at the top of the barometer tube is a vacuum and exerts no pressure on the mercury column.

The atmosphere pushes against the mercury bath, which in turn pushes the mercury up the tube. Hence,

$$\text{Pressure due to mercury column} = \text{Pressure due to atmospheric pressure}$$

The vertical height of the mercury column gives the required atmospheric pressure.

From Hydrostatic Pressure, we know that:

$$\begin{aligned} p_{air} &= p_{\text{mercury column}} \\ &= h \rho g \end{aligned}$$

,where h is the height of mercury column, $\rho$ is density of mercury, g is gravitational acceleration.

Length of Mercury Column at 1 atmosphere

We can compute the length of the mercury column if 1 atm ($1.013 \times 10^{5} \text{ Pa}$) of atmospheric pressure is acting on the mercury bath. The computation is as follows: (Density of mercury is $13.6 \times 10^{3} \text{kg m}^{-3}$)

$$\begin{aligned} p_{\text{1 atm}} &= \rho g h \\ 1.013 \times 10^{5} &= 13.6 \times 10^{3} \times 9.8 \times h \\ h &= 0.760 \text{ m} \\ h &= 76 \text{ cm} \end{aligned}$$

Barometers of Different Heights & Sizes

The figure above shows barometers of different heights and sizes. Since the principle behind the barometer is the phenomenon of hydrostatic pressure, we know that only the height of the fluid column is important in the determination of the pressure at the bottom. This means that the height, h in the above figure will remain unchanged if:

1. the glass tube is lifted up slightly from the dish
2. the glass tube is lowered further into the dish
3. the diameter of the glass tube increases
4. the glass tube is tilted
5. the quantity of mercury in the dish is increased.

Pressures at Different Heights of a Barometer

Let’s consider the figure above. We have:

• The pressure at $P_{a}$ is zero. (It is a vacuum in the air gap.)
• The pressure at $P_{b}$ is due to 26 cm of mercury.
• The pressure at $P_{e}$ is due to 76 cm of mercury.
• The pressure at $P_{f}$ is due to 84 cm of mercury.
• Pressure at $P_{b}$ and $P_{c}$ is at atmospheric pressure, i.e. 1 atm. Note: Technically, the pressure at $P_{c}$ is slightly lesser than $P_{b}$.
• Pressure at $P_{d}$ and $P_{e}$ is the same!

Characteristics

• Standard Atmosphere is the mean atmospheric pressure naturally existing at sea level on the surface of the Earth. It is equivalent to the pressure exerted by a vertical column of mercury (as in a barometer) 760 mm high or 101,325 Pa.
• If the mercury is replaced by water, the vertical column of water equivalent to the atmospheric pressure is approximately 10 m.
• The atmosphere pressure does vary from day to day and place to place.