Gasses

 

As already stated, gases are easily compressed and are indefinitely expandable. Gasses will expand to fill any volume that is made available to them. The properties of an expanding gas were examined by both Boyl and Gay Lussac which resulted in the enunciation of Boyl’s and Gay Lussac’s Laws. By experiment, Boyl showed that at a constant temperature the volume (V) of gas was inversely proportion to its pressure (P),

 

                               i.e.               

 

                                            where (K) is a constant 

 

Thus at constant temperature the product of the volume and pressure of a gas is constant.

 

Gay Lussac examined the effect of temperature on the volume of a gas and showed that the volume of a gas at constant pressure was proportional to the absolute temperature. The absolute temperature scale (or Kelvin scale) is one at which 0^o (0^oA or 0^oK) is that temperature where a body has minimum energy and can be no colder.

 

                          Thus,           

 

                Where (T) is the absolute temperature and  (K₂) is another constant.

 

Thus, at constant pressure the ratio of the volume of gas to the absolute temperature is a constant, which is Gay Lussac’s Law and/or Charles’ Law.

 

Combining Boyl’s Law and Ga Lussac’s law the general gas law is obtained,

 

 

Where (R) is known as the Gas Constant

 

In general if a fixed mass of gas at pressure (P₁) and temperature (T₁) having a volume (V₁) is changed to a temperature (T₂) and pressure (P₂), then

 

 

The above relationship is, of course, for a perfect gas but all natural gasses, as one might expect, deviate to various extents from the ideal case. A number of different modifications have been put forward to account for this ideality, but the most important is probably that developed by Van der Waal. Van der Waal tried to account for both finite size of the molecules and the interactive attractive forces between them. The interactive forces between the molecules () will reduce the effective outward pressure on the walls of the vessel which will be proportional to the masses of gas attracting and attracted each of which will be proportional to the gas density.

 

Now the density will be proportional to the inverse of the gas volume (v) and thus, 

 

 

where (a) is constant independent of the temperature.

 

Hence the.

Internal Pressure = External Pressure +  = 

 

In addition Van der Waal considered that the volume available to the molecules for motion was less than the actual volume by an amount equivalent to the volume of the molecules themselves (b). Thus the Van der Wall’s equation becomes.

 

The values for (a) and (b) are normally obtained experimentally. These laws can also be deduced from the kinetic theory of gasses.