# Boyles Law and pressure/volume relationships

Boyles Law states that, for any sample of gas, its pressure multiplied by the volume it occupies is a constant providing the temperature remains constant. (ie pV = constant). This is always true for perfect gases, for which pV = nRT by definition.

Real gases behave most like perfect gases at high temperatures and low pressures (as these are the conditions under which the assumptions of the perfect gas model are most closely obeyed). At atmospheric pressures, most gases obey Boyles Law to a reasonable approximation.

 Graphically, we may illustrate Boyles Law by plotting the values of p and V which satisfy the requirement for pV to be a constant. Each line must be plotted at one specific temperature, and is thus known as an isotherm. Note that the value of the constant depends upon the temperature, i.e. at higher temperatures the value of pV is larger than at lower temperatures:

However, we know that perfect gases and real gases do not behave in the same fashion, and the differences can be shown on a pV graph:

 The most noticeable deviation is that some portions of the graph are horizontal (meaning the volume drops rapidly for no pressure change). This is when the gas is becoming a liquid. During this time it is said to be at its vapour pressure. As we increase the temperature, we see that the vapour pressure increases. The black line bounding the horizontal lines marks the two-phase region; for any conditions of pressure and volume that lie within this region, both liquid and gas are present. Note the range of volumes over which the liquid and gas phases coexist (measured by the length of the horizontal portion of the isotherms) decreases as the temperature is raised, ultimately giving us one point (red dot), the critical point. Above this critical temperature, Tc, the gas cannot become a liquid, and is said to be a supercritical fluid.
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