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The Gas Laws: Charles' 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 Volume and Temperature, with Pressure Constant  
Consider a quantity of gas in a container of variable volume (as in Experiment 6TP)  
If the volume of the gas is measured at different temperatures while the pressure remains constant, the results are as shown by the graph below.  
   
Extrapolating the graph beyond the volume axis, as shown below, we can find the temperature at which the volume occupied by the gas should be zero.  
In practice, the volume occupied by the gas will, of course, never be zero: the molecules themselves have some (small) volume.  
The extrapolation will tell us the temperature at which the volume occupied by the gas, by virtue of the random motion of its molecules, will be zero.  
   
This suggests that the volume occupied by the gas (because of the motion of its molecules) would be zero at -273C.  
This suggests that this is the lowest temperature possible as it is the temperature at which the molecules stop moving.  
   
This temperature is (about) -273C.  
It is the absolute zero of temperature.  
As with the pressure law and the Boyle-Mariotte law, these results do not depend on the type of gas used.  
   
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 pressure, the volume is directly proportional to the absolute temperature.  
Therefore, we can write  
 
   
This conclusion is called Charles' Law (after French scientist, Jacques Charles)  
   
So, if a fixed mass of gas has initial (absolute) temperature T1 and initial volume V1 and final (absolute) temperature and volume T2 and V2 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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