TEMPERATURE AND THE PROPERTIES OF GASES 49 



pressures correspond to equally reduced temperatures, it is 

 possible to arrive at the values of some of the gaps in the table. 

 A value for the critical pressures of bromine found thus is 

 pc = 132. To arrive at approximate values for mercury, it is 

 necessary to make an independent estimate for either pc or Tc. 

 Since the ratio T B /Tc is also available, and taking this as 0-59, 

 Tc appears as 1065, and then from the known vapour densities 

 the critical pressure comes out at 95 atmospheres only. This is 

 remarkably low, and makes the ratio Tc/pc very large, thus 

 showing probably that v c is large. However, as has been 

 mentioned above, the data are still wanting to enable any 

 generalisations to be made with elementary substances and 

 simple compounds. 



To have complete knowledge of the thermodynamic condition 

 of a substance, it is necessary to know the quantity of heat which 

 will be required to raise a known mass of it a known difference 

 of temperature. In the case of solids and liquids, the mass is kept 

 under constant conditions of pressure and the volume allowed 

 to increase with increase of temperature, so that the applied 

 heat does external work in producing this increase of volume, 

 in addition to that which would be required to change its 

 temperature at constant volume. If we call Cp the atomic heat 

 at constant pressure and Cv that at constant volume, they will 

 mean the number of calories required to raise the atomic weights 

 of any substance one degree centigrade under these conditions. 

 However, to make the definition quite exact, it is necessary 

 to define the calorie used, as there is still unfortunately an 

 ambiguity owing to the existence of several calories which differ 

 by as much as 1 per cent. There is so much in favour of the 

 mean calorie, the hundredth part of the heat require to raise one 

 gramme of water from zero to ioo° C, that it is becoming more 

 generally accepted as the standard. We have, then, as p is 

 constant 



(13) Cp- Cv=p{v l - v) = $pv 



where ft is the coefficient of expansion at constant pressure. 



With solids and liquids Cp and fi can be measured, and Cv 

 can be deduced from them, as it is exceedingly difficult to measure 

 it direct. 



With gases and vapours, however, there is no difficulty in 

 keeping the volume constant, so that the two quantities Cp and 



4 



