Atmospheric Pressure

Objectives:

To learn the principles of measuring atmospheric pressure by constructing and using a water barometer, and comparing your results to pressure measured by a standard mercury barometer.

Background:

Atmospheric pressure has traditionally been measured using liquid in glass barometers. As is the case with many meteorological instruments, the traditional measurement means are still the most accurate, and mercury barometers are the standard where very accurate pressure measurements are required. The basic idea is to take a tube of liquid and turn it upside down in a pan of liquid. The level of liquid in the tube will run down the tube until the weight of the liquid column in exactly balanced by the weight of air in the atmosphere pressing down on the surface of liquid in the pan. By measuring the height of the column of liquid, one can measure the air pressure. (Remember that pressure is weight / area).

The relationship between the height of the liquid column and air pressure is given by the hydrostatic law applied to the liquid column:

$$\Delta \rho_{L}^{} \Delta$$ (6.1)

where the subscript ``L '' denotes ``liquid'', $\Delta$P_L is the pressure due to the liquid column; $\rho_{L}^{}$ is the density of the liquid; g is the acceleration of gravity (9.8 m s^-2 ) and $\Delta$Z_L is the height of the liquid column. If there is a perfect vacuum in the tube above the liquid column, then the air pressure = $\Delta$P_L . In most liquids the density $\rho_{L}^{}$ is a function of temperature so that usually temperature needs to be measured as well and a temperature correction applied to the measurement. This is certainly the case for mercury since the temperature dependency of mercury density is used for mercury thermometers.

One reason that mercury is often used in barometers is that the saturation vapour pressure of mercury at ordinary room temperatures is very low so that the assumption of a vacuum above the mercury is reasonable. In this lab we will be using water as our liquid. The saturation vapour pressure of water is not negligible and must be taken into account in computing the air pressure based on the height of a water column. In lab 6 we used a graph to find saturation vapour pressure (e^* ) as a function of temperature - we will need to refer to that figure in this lab.

Taking the saturation vapour pressure of water into account, the air pressure can be found from a water barometer as:

$$\rho_{w}^{} \Delta$$ (6.2)

where e^*_(T) is the saturation vapour pressure of water (refer to the humidity lab). The density of water ($\rho_{w}^{}$ ) at various temperatures is:

Temperature (o C)	15	17	19	21	23
Density - $\rho_{w}^{}$ (kg m-3 )	999.099	998.774	998.405	997.992	997.538	997.044

Equipment:

1. 12 m Plastic tubing with stopper and clamp for one end
2. Bucket
3. Water
4. Tape measure
5. Mercurial barometer with attached thermometer

Method:

Making a pressure measurement using the water barometer

1. In the lab carefully fill the tubing with water and seal one end with the stopper and clamp making sure not to let any air in the tube. (Do this under water in the bucket. Fill the tubing using the tap running slowly.)
2. Move to the lab rotunda with the tubing in the bucket of water and tape measure.
3. Work in groups of three. Have at least one member of your group remain with the bucket and tubing on the ground floor keeping the open end of the tubing immersed in water while other members of the group go up the staircase two floors.
4. Lower the rope from two floors up and tie it to the stoppered end of the water filled tubing. Pull the tubing up keeping the bottom end of the tube under water.
5. Measure the height of the water column with the tape measure with 0 at the water surface.
6. Measure the air pressure again using the mercury barometer (Remember to adjust for the temperature and gravity corrections).

Making a pressure measurement using the mercurial barometer

1. Adjust the level of mercury in the cistern by turning the brass screw so that the ivory pointer just touches the mercury.
2. Adjust the vernier scale on top so that the bottom of the scale just touches the top of the mercury meniscus.
3. Read the height in mm by lining up the line on the bottom of the vernier scale with the height scale on the right. Find the 10ths of mm using the vernier scale. ``(mm Hg)'' represents this reading
4. Make the temperature correction:
   • read the temperature from the thermometer on the barometer
   • using this temperature, find the multiplier (M) from the table on the wall next to the barometer
   • multiply the mercury height by this value: (mm Hg) x M = X
   • add this amount to the mercury height to find the temperature corrected mercury height: (T corr. mm Hg) = (mm Hg) + X
5. Make the gravity correction:
   • multiply the temperature corrected mercury height by +0.000766 and add the product to the temperature corrected mercury height: (TG corr. mm Hg) = (T corr. mm Hg) x 0.000766 + (T corr. mm Hg)
   • this value (TG corr. mm Hg) is the temperature and gravity corrected station pressure in mm of mercury
6. Convert from mm of mercury to Pa using the hydrostatic law:
   $$\Delta$$P = $$\rho_{{Hg}}^{}$$g$$\Delta$$Z
   where $\rho_{{Hg}}^{}$ = 13595.1 kg m^-3 , and g = 9.80665 m s^-2 .

Questions:

1. Find the air pressure using the water barometer.
2. Compare the value above with the pressure measured using the mercury barometer.
3. Compare with the pressure reading from the digital barometer located on the lab building roof. (Accessible on the internet, by going to http://nimbus.unbc.ca/wx/index.html, and clicking on ``text data''. The last two columns are station pressure and mean sea level pressure.)
4. Describe any sources of error in your pressure measurement using the water barometer.
5. One reason mercury is often used in barometers is that the vapour pressure of mercury is low so that the assumption of a vacuum above the liquid column is valid. What is at least one other reason why mercury is used as the liquid in barometers?