M. Achiile Cazin on Internal Work in Gases, 269 



I shall denote by 



dQ the heat supplied to the body when it undergoes an 

 elementary modification ; 



KdT the increase of its sensible heat, K being its true spe- 

 cific heat, and T = 273 + /° its absolute temperature (t in 

 Centigrade degrees) ; 



A the calorific equivalent of the unit of work ; 



dl the elementary internal work produced ; 



dYi the elementary external work produced. 



The general relation is 



dQ=KdT + AdI + AdV (1) 



The sum K dT + Ac?I is the differential of a function U which 

 has been called total internal heat by M. Zeuner, virtual energy 

 by M. Him. It is remarkable in this one thing, that its varia- 

 tions only depend on the initial condition and final condition of 

 the body, and not at all on the manner in which the change of 

 condition is effected. Its mechanical equivalent is still called 

 internal energy. 



For each body, there exists a certain relation, 



*(ft»,T)=0, (2) 



in which it is sufficient to have two of the three quantities p, v, 

 T in order that the condition of the body may be determined. 

 It is this relation which is expressed approximately, for the gases 

 called permanent, by the laws of Mariotte and Gay-Lussac, 



P Y = M > ( 3 ) 



M being a constant which depends on the units adopted and on 

 the nature of the gas. 



Thus the quantity d\J will be a function of two of the three 

 variables p, v, T (of v, T for example, considered as indepen- 

 dents) ; and when the body undergoes any final change we shall 

 have 



U-U o =0(t> 1J T 1 )-#> o ,T o ), 



whatever may be the law of the change between the initial con- 

 dition v , T , and the final condition v v T v 



It follows from this that the variation of virtual energy U— U 

 remains the same between the same limits, whether the mode of 

 change be reversible or non-reversible. 



Consequently from the two fundamental theorems of thermo- 

 dynamics, and from the experimental fact that for air a condition 

 exists in which relation (3) is verified, the following relation, ap- 



