PRIXCIPLES OF THE MECHANICAL THEORY OF HEAT. 271) 



lowinc" table, the values of the specific heat s, of the ahsolnte specific heat 7i", 

 and of the heat expended for internal work i. 



Silver... 

 Alimiiua 

 Copper.. 



Iron 



Lithium. 

 Katiium. 



Lead 



Sulpliur . 

 Ziuc 



0. 0570 

 0.214:i 

 0. 0949 



0. n;58 



0. 9408 

 0. 29:34 



0. o:{J4 



0. 1776 

 0. 0956 



0. 0222 

 0. 0875 

 0. 0378 



fi. 04:?o 

 0. :U2H 



0.104:! 

 0.0i2G 

 0. 0756 

 0. 0372 



0. 0348 

 0. 1263 

 0.0571 

 0. 0708 

 0. 5940 

 0. 1891 

 0.0183 

 0. 1020 

 0. 0583 



If we seek to ascertain in this way the value of k for carbon, we obtain, by 

 takini^ the atoniic weight 12 as a basis, 7t;=0.2, a value which is greater than 

 the value of s heretofore found for graphite and diamond. This circumstance 

 speaks decisively to the effect that, agreeably to llegnault's profiosition, we 

 sliould double the atomic weight of carbon and assume it to be equal to 24 ; we 

 then have, for the different forms of aggregation of carbon, the values of s, JCj 

 and i, exhibited in the following brief table : 



Charcoal. 

 Graphite. 

 Diamond 



0. 241 

 0. 174 

 0. 147 



-0.1- 



0. 142 



0. 074 

 0,047 



The inequality of the specific heat of different forms of aggregation of carbon 

 thus becomes intelligible, from the consideration that at a like elevation of tem- 

 perature the internal work performed is different, according as we are dealing 

 with diamond, graphite, or charcoal. 



In strictness, therefore, the law of Dulong and Petit Ls, in general, only valid 

 for the absolute specific heat /.', which, nndtiplied by the atomic weiglit of the 

 element, gives the constant product hp=^2A. The variations which the specific 

 heat of solid elements undergoes, when the temperature is raised, are likewise' to 

 be ascribed to a dillerence in the amount of internal work. 



In reference to chemically compounded substances, we have, for ascertaining 

 their absolute capacitij of heat K, the e(piation 



PK 



N 



=2.4 



(5), 



P-S 



•which is found from equation-—-- —a if we putK in the place of the experimen- 

 tally determined specific heat S, and the absolute specific heat of the element 2.4 in 

 the place of a. From equation (.'3) results K = 2.4 — . For water, for instance, 



we have N = 3, P = 16 + 2 = 1S: hence K = 2.4 ''^ =0.4; thus tlH> a))soluto 



specific heat of water in a solid, liquid, and gaseous form, is equal to 0.4. From 

 these ])remises we obtain, for the quantity of heat /, which, by an elevation of 

 temperature of 1°C., is expended in internal work, 



for ice . . . 

 for liquid water 



:0./5 — 0.4 = 0.1 

 1.0 — 0.4 = 0.0. 



