276 M. Achille Cazin on Internal Work in Gases. 



the preceding section, it is found that 

 T'=279°'44, 

 T,-T' = 3°-56, 



^=751-63 millims., 

 jbV= 391-27. 

 We have already had 



Hence p'v'=p v x is positive, and there is a production of ex- 

 ternal work during the efflux. This work has been produced at 

 the expense of the virtual energy of the gas ; and by that may be 

 explained why the fall of temperature T 2 -T' is greater than in 

 the first problem. 



Discussion of the experiments of Messrs. Joule and Thomson and 

 o/M. Hirn. 



Messrs. Joule and Thomson have made their experiments 

 under conditions in which the gas on leaving the orifice resumed 

 the initial temperature T y From that moment the sides fur- 

 nished to each unit of weight of the gas the heat CplTj— T ), C p 

 being the specific heat at constant pressure. We shall easily pass 

 from the preceding case to this latter. 



The gas was in the condition p\ v\ T'; it passes to the tem- 

 perature Tj and to the volume v" under the constant pressure p ; 

 hence it expands in producing external work /?>" -V) ; its vir- 

 tual energy experiences an increase 



KC^-TO+A f^ Tl (T J -p)dv. 

 The fundamental equation (1) gives therefore 



This equation may give v". But by adding equations (10) 

 and (8) together we get 



C^(T 1 ~TO=Ar'' Tl (Tj-^ + A(y^- Wl ). • (11) 



This formula reveals the final condition of the gas passing 

 from the condition p x ^ T, to the condition p' t/' T„ with 

 transmission of the external heat C^-T'). Moreover it is 

 immediately obtained by means of the fundamental equation (1). 

 In calculating it as I have done, there is the advantage of fol- 

 lowing gradually the operation under its two phases. 



In order to apply these formulae to carbonic acid, it is only 



