THE PROPERTIES OF METALLIC SUBSTANCES 403 



As was first pointed out by Wiedemann and Franz, 25 the thermal con- 

 ductance of metals at ordinary temperatures is very nearly proportional 

 to their electrical conductance. Subsequent investigations 26 have shown 

 that the ratio of thermal to electrical conductance is not a constant, but 

 increases with increasing temperature. Lorenz 2T showed that the ratio 



of thermal to electrical conductance - for pure metallic substances and 



H 



some alloys increases approximately as a linear function of the absolute 

 temperature, the coefficient being very nearly equal to the coefficient of 

 expansion of gases. Since the resistance varies approximately as a linear 

 function of the absolute temperature, it follows that the thermal con- 

 ductance of metals is relatively independent of temperature. At very low 

 temperatures, however, the thermal conductance of metals increases 

 markedly. Nevertheless, as K. Onnes and Hoist, 28 have shown, the 

 thermal resistance of metals does not approach a value of zero in 

 regions where metals are in the supraconducting state. For example, at 

 its melting point, the thermal conductance of mercury is 0.075; between 

 4.5 K and 5.1 K it is 0.27; and between 3.7 K and 3.9 K it is 0.40. 

 At very low temperatures, therefore, the thermal and electrical conduct- 

 ance do not follow a parallel course. 



The thermal conductance of alloys varies with composition in a man- 

 ner somewhat similar to that of the electrical conductance. The change 

 in thermal conductance, due to a given change in composition, is consid- 

 erably smaller than is the corresponding change in electrical conduct- 

 ance. The thermal conductance curves of alloys which form a complete 

 series of mixed crystals exhibit a minimum similar to that of the elec- 

 trical conductance curves. The relative decrease of the thermal con- 

 ductance, however, is much smaller than that of the electrical conduct- 

 ance. Accordingly, the ratio of the thermal to the electrical conductance 

 for homogeneous alloys is considerably greater than it is for pure metals. 

 Somewhat similar relations are found in the case of metallic compounds. 

 While compounds in general exhibit a lower thermal conductance than 

 do the pure components, the ratio of thermal to electrical conductance is 

 larger for the compounds than it is for pure metals. 



The thermal conductance of variable conductors is often as great as 

 that of typical metallic elements. Since the electrical conductance of 



these substances is relatively low, the ratio for these substances is often 



"Wiedemann and Franz, Pogg. Ann. 89, 497 (1853) ; ibid., 95, 338 (1895). 

 26 The literature relating to this subject has been collected in various handbooks; 

 see footnote, p. 385. 



27 L. Lorenz, Pogg. Ann. U{1, 429 (1872) ; Wied. Ann. IS, 422 (1881). 

 K. Onnes and Hoist, Proc. Amsterdam Acvd. 17 1 , 760 (1914). 



