274 M. Achille Cazin on Internal Work in Gases. 



It may be observed that 



jt^ =388*31, 

 j»V =392*06, 

 p v' = 396-30. 



Now the first and last of these products refer to the same 

 temperature T x ; and we have 



^= 1-0206, 



a number which accords very well with the experiments of M. 

 Regnault on the compressibility of carbonic acid. 



By comparing the initial condition and the final condition 

 before the calorific action of the sides, we get 



§ II. On the internal work which is accomplished in a gaseous 

 mass when it flows into the atmosphere under a constant pressure. 



Problem II. — A gas maintained under the constant pressure p v 

 and at the constant temperature T v flows into a space the sides 

 of which are impermeable to heat, where it is maintained at the 

 constant pressure p ! : to calculate the final temperature T' which 

 establishes itself beyond the orifice when the gaseous molecules 

 have lost their velocities in producing heat. 



This simple case refers to the experiments of Messrs. Joule 

 and Thomson and to those of M. Hirn. 



Conceive the gas to be contained in an indefinite cylinder 

 (fig. 9) divided into two parts by the partition E in which is the 

 orifice. In the permanent efflux there is on each side of the par- 

 tition a certain space in which the molecules of the gas acquire 

 velocity, and afterwards lose it in again forming heat. Let CandD 

 be the two planes which bound this space, and fju the gaseous mass 

 contained in it. Suppose the cylinders to have a section equal 

 to the unit of surface, and consider one kilogramme of gas under 

 the pressure p { and at the temperature Tj ; it will occupy a cer- 

 tain volume v J = AC. During the efflux the mass of gas 1+/a 

 passes from the condition AD to the condition CB, and the part 

 BD = z/ contains one kilogramme of gas at the temperature T' 

 and under the pressure p 1 . As in the two positions of the mass 

 1 +yL6 the part contained in the space CD remains in the same" 

 condition, we may say that one kilogramme of gas has passed 

 from the volume AC to the volume CB, and apply to this change 

 the fundamental formula of thermodynamics (1). 



We suppose that the sides of the cylinder are impermeable to 

 heat; then dQ = 0; consequently if external work has been 



