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The Gas Laws: The Pressure Law
The gas laws are the conclusions of experiments investigating the relation between the pressure, volume and temperature of a fixed mass of gas.  
   
As we have three variables, we will need three experimental investigations, in each case keeping one of the possible variables constant.  
   
The Relation Between Pressure and Temperature, with Volume Constant  
Consider a quantity of gas in a container of constant volume (as in Experiment 5TP)  
If the pressure exerted by the gas is measured at different temperatures, the results are as shown by the graph below.  
 
Extrapolating the graph beyond the pressure axis, as shown below, we can find the temperature at which the pressure exerted by the gas should be zero.  
 
This temperature is (about) -273C.  
As with Charles' law and the Boyle-Mariotte law, these results do not depend on the type of gas.  
 
According to the kinetic theory of matter, the pressure of a gas is due to the motion of its molecules and, since temperature is a measure of the average kinetic energy of the molecules, we must assume that at this temperature, the molecules have stopped moving.  
We therefore suggest that -273C is the lowest temperature possible.  
It is the absolute zero of temperature.  
   
This gives us the Kelvin or absolute scale of temperature.  
 
Temperatures on this scale are written TK, without any "degree" symbol.  
Thus 0C becomes 273K, 100C becomes 373K etc.  
   
Note that the absolute zero of temperature has not been attained in practice*; it is a theoretical prediction found by extrapolation of experimental results.  
   
Now that we have shifted the vertical axis of our graph and obtained our new temperature scale, we will state the following "gas law":  
For a fixed mass of gas, at constant volume, the pressure is directly proportional to the absolute temperature.  
Therefore, we can write  
 
   
Slightly unusually, this law is not named after anybody in particular and is know rather boringly as... the pressure law.  
   
So, if a fixed mass of gas has initial (absolute) temperature T1 and initial pressure p1 and final (absolute) temperature and pressure T2 and p2 respectively, we can write  
 
 
*however, the lowest temperature attained (at the time of writing; 03/02/2017, at about 17h29) was at Helsinki University (where it's often pretty cold to start with) when a piece of rhodium metal was cooled to 0.1nK or 0.0000000001K... quite chilly!  
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