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) 273°C. 

As with Charles' law and the BoyleMariotte
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 273°C 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 0°C becomes 273K,
100°C 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 T_{1} and initial pressure p_{1} and
final (absolute) temperature and pressure T_{2} and
p_{2} 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! 
