[ 52 ] 



V. A Note on the Relation between the Thermal Conductivity 

 and the Viscosity of Gases with reference to Molecular 

 Complexity. By J. A. Pollock, D.Sc, Professor of 

 Physics in the University of Sydney *. 



IN the equation k=fr)c v , expressing the thermal conduc- 

 tivity of a gas in terms of the viscosity and specific 

 heat, the coefficient / is a numerical factor which is approx- 

 imately constant for gases of the some atomicity. Such a 

 fact suggests the probability of a relationship between /and 

 7, the ratio of the specific beats. But long before the result, 

 just mentioned, was fully established, the probability of f 

 being a function of 7 was recognized, though it was 

 not generally appreciated. As early as 1876 Boltzmannf, 

 from theoretical considerations, obtained the expression 

 /=3/ / (7 — 1)/2, where f is the constant for monatomic 

 gases. It has been known for some time that the equation is 

 physically inaccurate, but the matter does not seem to have 

 been followed further. 



Recently new results for the thermal conductivities of a 

 number of gases have been published by Eucken {. In con- 

 nexion with these measures, Eucken discusses the dependence 

 of /, not only on the properties of the molecule, but also on 

 the temperature. As possibly lying outside the main lines of 

 his investigation, he does not consider the relationsip of / to 

 7, but, from the zero temperature values of the thermal con- 

 ductivities and viscosities given by him, a relation appears to 

 exist between the two factors which can be expressed by an 

 equation of the form 



0(7-1) 

 I- If ' 



where a and n are constants. The precise arithmetical 

 adjustment of these constants may well await further 

 measures ; in the meantime, with numerical simplicity as 

 well as physical accuracy in view, the equation may be 

 written 



7-32(7-1) 



If, in the original expression, w, the power of 7, is put 



* Communicated by the Author. Read before the Royal Society of 

 N. S. Wales. 



t Boltzmann, Pogg. Ann. clvii. p. 457 (1876) ; see also Schleiermacher, 

 Wied. Ann. xxxvi. p. 346 (1889) ; and Chapman, Trans. Roy. Soc. 

 ccxi.A. p. 433 (1912). 



% Eucken, Phys. Zeitschr. xiv. p. 324 (1913). 



