416-419] Numerical Values 343 



molecules inside a solid or liquid are subjected to a pressure of which the 

 amount, measured by ordinary standards, seems enormous. The molecules, 

 then, may be said to be pressed together by one another's attraction, and so 

 to occupy less space in the solid or liquid state than they otherwise would. 



To form a numerical estimate of the amount of this compression, let 

 us consider the process of changing water initially at into steam, the 

 pressure being atmospheric pressure throughout. To raise the water to 

 boiling point. 100 units of heat are required per gramme. This heat does 

 not change the density of the water to any great extent, so that only a small 

 fraction of the 100 units will be spent in doing work against the inter- 

 molecular forces. To change the water at 100 into steam at 100, we now 

 require 537' units of heat per gramme. Of this heat, part is spent in doing 

 external work, and part in overcoming the attractive forces between the 

 molecules. The former part can easily be calculated. A gramme of steam 

 at 100 occupies about 1647 cu. cms., so that the external work done per 

 gramme of steam is equal to the product of the atmospheric pressure by 

 1646. In c.G.s. work-units this is found to be 



1*668 x 10 9 c.G.s. work-units. 



Dividing by 4'22 x 10 7 to reduce to heat-units, we obtain 



39'52 c.G.s. heat-units. 



Hence of the 537 heat-units per gramme required, about 40 are spent 

 in external work, and therefore about 497 in overcoming intermolecular 

 attractions. This is equal to 2*1 x 10 10 work-units, and therefore if spent 

 in increasing the translational energy of the molecules, would be equivalent 

 to a rise of temperature of 



2 21 x 10 10 



3 R/m 



or about 3000 C. It' must, however, be borne in mind that in a liquid 

 each molecule is " compressed " at more than one point of its surface. If, 

 as a rough guess, we assume contact at ten points, the rise of temperature 

 just calculated must be divided by ten. The " compression " of molecules 

 in water is therefore about equal to that of molecules in collision at a 

 temperature of about 300 C. 



Other substances might be similarly treated. It would be absurd to 

 apply the empirical temperature-correction over so large a range of tem- 

 perature, and under such different physical conditions, but it is obvious 

 that the difference between the two values for \v is sufficiently explained. 

 As regards order of magnitude of the correction, an examination of the table 

 on p. 256 will be of use. 



419. There is a further consideration which is capable of reconciling to 

 some extent the discrepancies between the two sets of figures given on 

 p. 341. If we arrange the substances there given in the order of the 



