4o6 



JVA TURE 



[August 27, 1908 



gfas becomes zero must be siiyiply the temperature of abso- 

 lute molecular rest, and, therefore, will be the absolute 

 zero. From the properties of such a gas its absolute tem- 

 perature could at once be experimentally determined, if 

 only such a gas were available for experiment ; for 

 it would come out as the reciprocal of its coefficient of 

 expansion. But as a perfect gas is not available, an im- 

 perfect gas has to be employed, and a correction made for 

 the amount of its imperfection ; the amount of this cor- 

 rection being deduced by reasoning based on its behaviour 

 when subjected to an irreversible operation. For instance, 

 it may be allowed suddenly to expand adiabatically in such 

 a way as to do no external work, and, therefore, not to 

 cool itself if it were perfect, provided time is allowed for 

 all eddies and streaming motions to subside ; and we may 

 then observe the actual consumption of heat or fall of tem- 

 perature really produced — which would be proportional to 

 the cohesion multiplied by the change of volume. The 

 change of temperature so observed is the chief term in a 

 correction to be applied to the reciprocal of the observed 

 coefficient-of-expansion-under-constant-volume of the im- 

 perfect gas. 



The experiment as first made by Gay-Lussac, September, 

 1806, and later independently and more exactly by Joule, 

 of allowing a gas to double its volume inside a closed 

 vessel, by opening a connection between a full and an 

 empty portion of a vessel, was manifestly an interesting 

 and suggestive experiment, and a check or verification of 

 Mayer's hypothesis that the mechanical equivalent of heat 

 could be obtained by equating the heat supplied and the 

 work extracted from expanding air ; but the full meaning 

 and bearing of such an experiment is bv no means obvious, 

 and it is remarkable that it should lead to a determina- 

 tion of the zero of absolute temperature. For this pur- 

 pose it has to be repeated in a more refined form — the 

 oozing of gas as a steady stream from high pressure to 

 low through a porous plug — and a determination made 

 of the change of temperature resulting, when all eddies 

 and organised kinds of motion have subsided, and when 

 everything has become heat again, except what was lost 

 in internal work. 



It is well known now that the practical liquefaction of 

 gases depends on this very efTect ; for, of course, without 

 some cohesion between the molecules liquefaction would 

 be quite impossible. The essence of liquefaction is the 

 automatic subdivision of the contents of a vessel into two 

 sharply bounded regions of different density, and the re- 

 taining of them in this condition for a time by internal 

 molecular forces. 



Absolcte Temperature. 



The elementary argument about the notion of absolute 

 temperature in terms of a perfect gas can be put thus : — 



A perfect gas is one the molecules of which act on each 

 other, and on the walls of the containing vessel, solelv by 

 bombardment. Simple mechanics shows that such a sub- 

 stance exerts a pressure — 



3 



(U 



and whenever it expands all the work done is against ex- 

 ternal pressure. 



The heat in such a body is solely the energy of its ir- 

 regular or unorganised molecular motion — including rota- 

 tion as well as translation ; and the temperature of such a 

 body can be defined as simply proportional to the heat, or 

 equal to the heat divided by a capacity-constant inc. 



If the gas has to expand against external pressure, more 

 heat must be supplied to allow for the external work done. 



/ 



^dv; the capacity being now called mc' if the pressure is 



constant. Consequently, if the gas be heated at constant 

 pressure, from absolute zero up to the temperature T, the 

 heat required can be expressed as — 



Yi-mcT-Vpv = mc"Y ; 



wherefore — 



p=fU'-cXl 



(2) 



which may be called the characteristic equation of the 

 substance. 



NO. 2026, VOL. 7S] 



Comparing this with the first equation, we see that — 



»'^ = 3(/-.)T (3) 



which constitutes a definition of absolute temperature in 

 terms of the characteristic constant c' — c; the " 3 " having 

 reference to the three dimensions of space. 



Actually to determine T we can employ equation (2), 

 and can get rid of the constant, say, by measuring the 

 increase of pressure when the gas is heated at constant 

 volume. This gives — 



/ T' 

 or — 



T=/^=i (4) 



the reciprocal of the coefficient of expansion. 



In other words, the expansibility of a perfect gas is 

 simply the reciprocal of its absolute temperature. 



This is consistent with the form of characteristic equa- 

 tion which allows for molecular bulk, though not for mole- 

 cular forces — namely, p{v — b) = RT. 



For a slightly imperfect gas there is the cohesion or 

 molecular-attraction term to be attended to as well, and 

 its characteristic equation is — 



{/■ + K){v-6) = -RT, 



K being a function of volume only. For constant-volume 

 warming this gives — 



dp _dr 

 / + K T' 



or — 



■^ dp dp 



or — 



HH) ■■•••■«> ) 



where a is the coefficient of expansion as measured on a 

 constant-volume thermometer ; showing that a correction 

 factor not far from unity must be applied, depending on 

 the incipient cohesion or inter-molecular attraction, repre- 

 sented by Laplace's K or van der Waals's Ap^. 



To get K we must perform a definite operation, say a 

 sudden expansion 5v, under adiabatic conditions, allowing 

 no external work to be done ; and we must observe the 

 resulting absorption of heat, say by noticing the small 

 change of temperature 5T. It would be zero if the gas 

 were perfect. If imperfect, the energy lost is Kiv. 



To ensure that no external work is done, the operation 

 must be performed in a rigid vessel, and a steady stream 

 of gas will carry off the defect of heat 5H. The cooling 

 will then be due only to internal work K5tj ; and the heat 

 change can be expressed as mc'ST, when eddies have sub- 

 sided. 



Thus we get— 



KSv = SH = mc'ST = vp,'dT ; 



but now instead of 5-' we may write - - Sp, since the tempera- 



/ 

 ture is nearly constant, so that — • 



K 



'^5T 



(6) 



Hence, denoting by 6 the small observed change of tem- 

 perature corresponding to the change of pressure n, and 

 substituting (6) in equation (5), we get finally as an ex- 

 pression for the absolute temperature of the gas experi- 

 mented on — ■ 



=K->3 



T = i 



(7) 



Perhaps the equation looks still clearer if we write it in 

 terms of the volume of air v streaming through the porous 

 plug, down the difference of pressure 5/>, and carrying 

 with it ultimately the defect of heat 5H, measured any- 

 how ; for then — 



