M. Achille Cazin on Internal Work in Gases. 281 



§ III. On the internal ivork in a gas which undergoes expansion 

 or compression without external calorific action, and of which 

 the elastic force at each moment balances the pressure exerted on 

 its surface. 



Problem III. — A kilogramme of gas at temperature T, passes 

 from volume v Y to volume v 2 while overcoming external pressure 

 equal at each moment to its elastic force, without there being 

 either addition or loss of external heat : knowing v ls Jfj, and v 2 , 

 to calculate the final temperature T 2 and the internal work 

 effected. 



This operation belongs to the kind which are termed rever- 

 sibles. It cannot be realized in practice ; but a gaseous mass 

 which pushes a piston in a cylinder, or which is compressed by 

 the piston so quickly that the external heat may be neglected, 

 comports itself very nearly as in the problem enunciated. 



The quantity of external heat which the gas takes in changing 

 its condition may be represented by 



Q=JT^, 



<j> being a function (of two of the variables p, v } T) which Mr. 

 Rankine has called the thermodynamic function. 

 If v and T be taken as the variables, we have* 



■0 = KCT + Afj^<fo, 



dip 



■4m being the partial derivative of p deduced from relation (2). 



In the present problem Q = 0; hence <j)= constant, and con- 

 sequently 





KC^+A ' 3>=0 (16) 



This equation being combined with relation (2), T 2 may be 

 calculated when T 1? v v v 2 are known. The initial and final pres- 

 sures^,, p% may be calculated by means of relation (2). 



A relation between p and v may afterwards be established, 

 which will serve to calculate the external work 



'»2 



pdv. 

 Finally, the internal will be 



r 



a:n ->>■ 



Hence the problem is solved. 



* P. de Saint-Robert, Principes de Thermodynamique, p. 69(1865), 

 Phil. Mag. S. 4. Vol. 40. No. 267. Oct. 1870. U 



