and its relation to Latent Heat. 15 



their constituent chemical elements, because the application of ex- 

 treme heat alone is capable of eflfecting their complete separation. 



§ 16. The work expended (and its equivalent of heat made 

 latent) in causing the same absolute increment of volume, dimi- 

 nishes as the volume increases. The evidence in favour of this 

 is as follows : — At the boiling-point water expands -0008 in volume 

 for 1° C, and -^-Q^hs of a deg; c-e are rendered latent — are expended 

 in performing the work of expansion ; hence if the same rate 

 holds good up to the transition point, when the hquid volume is 

 at least double, the quantity of heat required to effect such ex- 

 pansion would be 875°. But the latent heat is only 537°. 



At its boiling-point alcohol expands -0013 per 1°, and /oths 

 of a degree are rendered latent. At transition-point the volume 

 is doubled. This, at the rate of -0013 per 0"-7, would require 

 540 C. degrees of the specific value of the heat of alcohol, or 345 

 if of the value of the specific heat of water. The latent heat 

 is only 209. Thus it appears that the increment of volume 

 corresponding to constant decrement of latent heat must increase 

 as the liquid expands. 



§ 17. I may here remark, that the curve traced out by the expan- 

 sion of alcohol from —32° C. (observed by ]\[. Pierre, Ann. de 

 Chim. vol. XV. p. 354) up to the point of transition agrees remark- 

 ably well with the hyperbola, so as to admit of its equation being 

 employed as an empirical formula. This is also the case with 

 sulphuric aether, turpentine, sulphuret of carbon, and some 

 other anhydrous liquids, including mercury. 



The form of the equation is {v — h)[a—t) = c"; in which v is 

 the volume, t the temperature by air-thermometer reckoned from 

 the zero of gaseous tension, b, a, and c- constants that may easily 

 be computed from three observations. 



& 18. There are hardly sufficient data at present fully to test 



the equation m^=( ^-yr- ) [§ 13] for the same liquid at difi'erent 



temperatures ; but it may be of advantage to follow the analysis, 

 and trace out what arc the relations amongst the data that are 

 required by it. 



As the volume of the molecule must be assumed to increase in 

 correspondence with the volume of the liquid, the expansion of 

 the liquid supplies the exact value of the differential of the left 

 side of the equation at any temjierature within certain limits. 



At a givLu temperature, and for a constant increment of tem- 

 perature, we have 



m L ti ' 



QL 



