Determination of Chemical Constants. 3 



means of Debye's formula or Nernst-Lindemann's formula, 

 and for temperature T higher than (/3ujT = l) it makes an 

 inappreciable difference which of the two is employed. 



The integration of the conversion term, derived from 



9u 2 vT 



c p = c v + — ~ (where a is the linear coefficient of expansion, 

 tc 



v the atomic volume, and tc the compressibility), is not 



so readily obtained. But it has been found sufficiently 



accurate to assume that c p = c v + aT 3/2 , as suggested by 



Magnus and Lindemann (Z. Elektrochem. xvi. p. 269, 



1910). As ^5 = aT 3 / 2 , it follows «ocT 1/4 , and this has 

 tc 



been found to be approximately the case over a wide 



range of temperature for such substances as copper and 



silver, where the variation in coefficient of expansion with 



temperature has been measured. This holds at ordinary 



temperature up to fairly high temperatures. On the other 



hand, at very low temperatures where c y = aT 3 , a will 



vary as T 3 , provided, as is probable, — is a constant. The 



v 



tc 



term aT 3/2 is a useful approximation, and the constant a 

 ean be obtained either from measurement of a, v, and tc 

 at a definite temperature, or from the specific heat mea- 

 surements compared with those calculated 'from Debye's 

 formula. 



The formula (1) given above, on integration, becomes 



+ 3/2 [ln(/"/ T -l)-f ln(^ 2T -l)]-A . « . w+i, 

 which may be written more conveniently : 



\ogp 



4-571 



^^fi-im 



- 0-0583 «T 3 / 2 +C, . (2) 

 where Ihe term* 



[ At - A °~] =-JR. fj • $-ln(^-l)^ln(>AT_i)-|. 



* The values of -1~ At ~ A u ~| and ["-JlzILo"! for different values 



of j8v/T are given in Pollitzer's ' Die Bevechnung Obemisciier Affinitaten ' 

 1912, and the corrections to be introduced due to use of Debye's equation 

 instead of the Nernst-Linderaann equation are to be found in Hitaber. 

 Akad. Wiss. Hi. p 1176 (1912). 



B 2 



