The barometer

Demonstration

This introduces the barometer tube and the pressure exerted by the Earth’s atmosphere.

Apparatus and Materials

• Barometer tube
• Trough
• Metre rule
• Mercury tray i.e. large non-metallic, smooth-surfaced tray (ideally with a small drain hole in one corner fitted with a rubber bung), 2
• Translucent screen and lamp
• Retort stand, boss, and clamp
• Mercury
• Small plastic funnel

Health & Safety and Technical Notes

Read our standard health & safety guidance

Mercury vapour is very toxic but the liquid evaporates very slowly. Provided any spilt mercury is collected thoroughly, this demonstration can be done in a lab with normal ventilation. It is helpful to have two mercury trays: one on the floor for filling the tube over, and one on the bench for the barometer itself. See CLEAPSS Lab Handbook section 12.13.2 for tips.

When filling a closed tube as described below, it helps to first fill the tube until it is nearly full, up to a few centimetres of the open end. Close this open end with a finger and tilt the tube to run the air bubble very slowly to the other end of the tube and back. It will collect up any small, sticking bubbles on the way. Then fill the tube to the top.

The whole experiment could be done in front of the translucent screen and lamp. This will make it clearly visible to the class by silhouetting against the bright background.

An alternative to this method is to have an open-ended tube. One end is dipped into a dish of mercury, the other is connected to a vacuum pump, and the air evacuated. Note that if you do this, you will need a trap consisting of a strong round-bottomed flask inserted between the pump and the vertical tube. This prevents mercury entering the pump in the event of an accident.

Procedure

1. Fill the barometer with mercury, holding it over the tray throughout.
2. Hold a finger on the open top of the full tube and invert it into a trough of mercury. Do not remove your finger until the end of the tube is below the surface.
3. Hold the barometer in a clamp to measure the height of the mercury column.
4. Daily pressure measurements can be made with the barometer stored safely in a fume cupboard.

Teaching Notes

• Students need to understand that the air pressure on the mercury in the bowl balances that exerted by the column of mercury in the tube.
• Some students will just need to grasp that the bigger the air pressure, the higher the column of mercury. Others will cope with the argument that the pressure exerted by the column = weight of column/area on which it sits.
  • The weight of the column
  • = mass of column x g
  • = density x volume x g
  • = density x height of column x area x g
  • So air pressure = density x height of column x area x g /area = density x height of column x g
• This could lead to some thought-provoking questions:

We live at the bottom of an ocean of air and air molecules create the air pressure by bouncing onto the surface of the Earth. The air pressure on the mercury outside in the bowl pushes the mercury up inside the barometer tube and the column of mercury just balances the air pressure. Now, imagine that we live in an atmosphere of mercury instead of air. How high would the mercury have to be from the floor to the top of the atmosphere if that was all there was to make the pressure that we actually live in down at the floor? Yes the height would have to be the barometer height, about 75 cm of mercury.

Now think about the real atmosphere. How high would that have to be if it went on up and up just as thick as the air is in this room and then stopped at the top of the atmosphere and there was nothing more above? How high would that atmosphere of air have to be to make the pressure we measure here?

An atmosphere of mercury would have to be 75 cm high, the same height as the mercury barometer height; because that is the height of mercury which can press on the base of anything with the same pressure as the whole atmosphere. How high would a water barometer have to be? We would need to know the density of water compared with mercury. So now we must go and find that comparison.

Finally, how high would the atmosphere have to be to balance a mercury barometer or a water barometer? We would need the density of air compared to that of water or mercury.

• Students capable of using equations of motion could work out how fast an air molecule would be moving as it reached the surface of the Earth, after falling from the top of this ocean/atmosphere and passing through the gaps between the other molecules. The result obtained will be about 20% below the actual average speed of air molecules (500 m/s).
  • This can lead to a useful discussion of estimates and the assumptions on which they are based. Also, to give it some respectability, this method was used by Boltzmann to arrive at the Maxwell distribution, with a modification for the uniform density assumption.
  • For example: If the height of a uniform atmosphere of air is approximately 8 km,
  • Then using the kinetic equation v² = u² + 2 as
  • The velocity at the Earth's surface is √(2 x 10 x 8 x 10 ³ )= 400 m/s
• Students who know pV = 1/3 nmv ² or p = 1/3 ρ v² will be able to calculate the velocity of air molecules at the Earth's surface.
• This is an astounding result; faster than a small rifle bullet and over 1000 miles an hour. Of course some air molecules are travelling faster than that and others more slowly. 500 m/s is just the average speed.
  
  The reason why gas molecules have a great variety of speeds is that they are frequently colliding with each other and exchanging kinetic energy in collisions so that a molecule sometimes travels faster and sometimes slower. Of course the whole lot keep the same total kinetic energy all the time. The speeds have a statistical distribution around a constant average which is characteristic of the temperature as shown in the diagrams.

This experiment was safety-tested in July 2006