32 SCIENCE PROGRESS 



A very slight consideration of the above conditions which 

 would have to be satisfied by an equation of state show that 

 it must necessarily be very complex if it is to express them 

 exactly. Suitable equations can be obtained as the result of 

 careful experiment under known conditions and over a definite 

 range for certain given substances, but such measurements are 

 difficult and lengthy, and the values found are only strictly 

 applicable to the conditions under which they are made. 



These measurements, although of the utmost importance in 

 special cases, would be of little assistance in the general question 

 without a guiding principle. The utility of this can be best 

 illustrated by an example. Consider some hydrogen and some 

 carbon dioxide at the ordinary temperature and under the 

 atmospheric pressure. For small changes of pressure and 

 temperature, both will behave very similarly. Suppose, how- 

 ever, that they are strongly compressed. It will be found that 

 at 1 5 C. the carbon dioxide will become a liquid under a 

 pressure of 51 kilogrammes per sq. cm., whereas the hydrogen 

 will become very dense, but will still remain a gas even under 

 the enormous pressure of 5,000 kilogrammes per sq. cm. as 

 found by actual experiment, and as we know now under any 

 pressure which could be applied at this temperature. The 

 former is called a vapour, the latter a gas at this temperature, 

 and to bring hydrogen into the condition of a vapour it is 

 necessary to go down to the temperature of about — 240 C. 



It is found that there is some particular temperature for 

 every gas, below which it must be cooled before it can be 

 liquefied, and which is known as the critical temperature (Tc) 

 while the necessary pressure to liquefy at this temperature is 

 the critical pressure {pc). The significance of this point will 

 be further illustrated by a consideration of the result of heating 

 a liquid and the vapour above it in a space where pressure 

 can be applied. At any temperature there is a definite vapour 

 pressure under these conditions which is independent of the 

 volume of liquid and vapour until there is either all liquid 

 or all vapour. As the boiling point is that at which the vapour 

 pressure of the liquid is the same as the pressure above it, 

 it follows that as the pressure on a liquid is reduced from the 

 normal boiling point under atmospheric pressure the liquid will 

 boil at continually lower temperatures until, in the natural 

 course, the freezing point is reached, when it changes to the solid 



