TRANSACTIONS OF SECTION B. 831 



FRIDA Y, SEPTEMBER 9. 



The following Papers aud Report were read : — 



1. Some Researches on the Thermal Properties of Gases and Liquids. 

 By Sydn^et Young, D.Sc, F.E.8., tfniversity College, Bristol. 



Gases uuder moderate or low pressures are characterised by the simplicity 

 of the laws relating' to the variation of their volume witli tempei'ature and 

 pressure. But when the pressure is great!)' increased, these laws no longer hold 

 jgood ; at constant temperature the product pr, instead of remaining constant, 

 diminishes until a minimum is reached, and at still higher pressures increases 

 again, and this increase continues up to the highest pressures that have been 

 reached. 



A most important advance in the explanation of the behaviour of compressed 

 gases and of liquids was made just twenty-five years ago by Van der Waals, 

 who, taking into account the two facts (1) that the molecules of a gas attract one 

 another, (2) that they occupy a finite volume, and are not mere mathematical 

 points, proposed the formida 



{p+ ^,) (.v-b) =RT 



in place of the simple one ^y = RT. The formula of Van der Waals expresses 

 very well the general relations of pressure, temperature, and volume for hoth 

 gases and liquids, but does not give the actual values with sufiicient accuracy, 

 and many attempts have heen made to alter it in such a way as to bring about 

 a better agreement. It is noticeable that at constant volume the formula becomes 

 ^ = KT — c, where K and c are constants, depending on the volume, and this 

 simple relation has been found to hold good for gases by Amagat, and for both 

 gases and liquids by Ramsay and myself. Within the Inst lew years I have 

 investigated the behaviour of a hydrocarbon, isopentane,' through a very wide 

 range of volume (1'6 — 4000 cc. per gram), and of normal pentane through a 

 smaller range, and the data so obtained have led Rose-Innes ^ to a formula 



p=^\l^ ? \ ^ 



V { v + k—gv-"^] v{v + k), 



based on the simple one p = KT - c, which reproduces the observed isothermals 

 from the largest volume to about 3-4 cc. per gram, with a maximum error of 

 .slightly over 1 per cent. 



A complete investigation of this kind requires, however, a large amount of 

 time, and can only be carried out with very stable substances of comparativelv 

 low critical temperatures ; and it occurred to me about eleven years ago that a 

 careful study of certain generalisations, deduced by Van der Waals from liis 

 formula, might yield valuable results, and perhaps indicate the direction in whicli 

 the formula requires alteration. 



The generalisations may be stated thus : — If any two substances, A and C, 

 are compared at pressures, P^ and Pj,, proportional to their critical pressures, tt^a 

 and 7r,,„, their boiling points (absolute temperatures), T^ and Tg, will be propor- 

 tional to their critical temperatures, ^^a and 6^^^, and their volumes, both as liquid, 

 Va and Vb, and as saturated vapour, V/, and ru, will be proportional to their 

 critical volumes, ^^a and 0oe- It would follow from this that at ' corresponding ' 

 pressures the ratios of the actual to the theoretical density of saturated vapour, 



^, should be the same for all substances. 



It is convenient to speak of the ratio of the pressure to the critical pressure as 

 the ' reduced ' pressure, it, the actual pressures, Pa, Pb, being called ' correspond- 

 ing ' pressures. 



' Proc. Phys. Soc, vol. ziii. p. 602. 

 * Ihid., vol. XV. p. 126 ; vol. xvi. p. 11. 



