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Atmospheric Pressure
There are many ways to demonstrate the existence of a pressure due to the atmosphere.  
Perhaps the easiest is to remove the air from a plastic water bottle.  
The bottle collapses due to the pressure of the air around it.
Another amusing trick is shown below.  
   
 
Completely fill a test tube (or similar container) with water.  
Place a small piece of paper over the end and then turn the tube over.  
The paper will stay in place, held by atmospheric pressure.
If the paper is removed carefully, the water stays in the tube, again, held in by the pressure of the air surrounding it (a steady hand is needed!).  
   
Measuring Atmospheric Pressure  
Imagine doing something similar to the trick described above but with mercury in place of the water.  
However, this time put the inverted tube into a reservoir of mercury, as shown below.  
   
 
The pressure of the atmosphere (represented by the red arrows) keeps the mercury in the tube.  
However, this is only possible if the pressure due to the atmosphere is strong enough to support the weight of the mercury. Remember that mercury is a very dense liquid, about 13.6 times as dense as water.  
If we repeat the experiment with a much longer tube, the situation will be as shown in the next diagram.  
   
   
In this case, the mercury falls until the pressure due to the weight of the mercury column (acting at the level of the surface of the mercury in the reservoir) is just equal to the pressure exerted by the atmosphere.
 In other words, the height, H, gives us a measure of the strength of the atmospheric pressure.
 
If the pressure of the air increases, a little more mercury will be pushed into the tube and H will increase.
 
The instrument shown in the diagram is called a mercury barometer.
Normal (or standard) atmospheric pressure is strong enough to support a column of mercury 760mm high.
This explains why pressures are often stated in mmHg.
We say that normal atmospheric pressure is equivalent to 760mmHg.
Alternatively, a pressure of 760mmHg is called 1atmosphere.
 
   
If a gas is said to be at standard temperature and pressure, s.t.p. (or normal temperature and pressure, n.t.p.), this means it is at 0C and 760mmHg.  
   
Using the equation developed here , you can show that a pressure of 760mmHg is equivalent to about 105 Nm-2, that is, equivalent to the weight of about 10 tons of mass on each square metre!  
   
Why do we choose to use mercury in a barometer rather than, say, water or oil?  
A mercury barometer is already quite a big instrument... how big would a water barometer be?  
   
(About 13.6 times higher! because mercury is about 13.6 times as dense as water.)  
   
Measuring Pressure Differences  
The difference between two pressures can be measured using a manometer.  
The simplest type of manometer is a "U" shaped tube with some liquid in it.  
The diagram on the left below shows the situation in which the two pressures are equal.  
 
On the right, we see that either pressure p1 has increased or pressure p2 has decreased (could be both, I suppose).  
The liquid levels settle down when enough of the liquid has been lifted up such that (considering pressures in mm of the liquid concerned)  
 
Note that a manometer tells us nothing about the individual pressures p1 and p2 , only the difference between them.  
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