84* Prof. Clansius on the Internal Work 



passage from a lower to a higher temperature as a negative 

 transformation. 



If we represent the transformations which occur in a circular 

 process by these expressions, the relation existing between them 

 can be stated in a simple and definite manner. If the circular 

 process is reversible, the transformations which occur therein 

 must be partly positive and partly negative, and the equivalent 

 values of the positive transformations must be together equal to 

 those of the negative transformations, so that the algebraic sum 

 of all the equivalent values becomes =0. If the circular process 

 is not reversible, the equivalent values of the positive and negative 

 transformations are not necessarily equal, but they can only differ 

 in such a way that the positive transformations predominate. 

 The proposition respecting the equivalent values of the transfor- 

 mations may accordingly be stated thus : — The algebraic sum of 

 all the transformations occurring in a circular process can only be 

 positive, or, as an extreme case, equal to nothing. 



The mathematical expression for this proposition is as follows. 

 Let dQ be an element of the heat given up by the body to any 

 reservoir of heat during its modifications (heat which it may 

 absorb from a reservoir being here reckoned as negative), and T 

 the absolute temperature of the body at the moment of giving 

 up this heat, then the equation 



f f =o (I.) 



J 



must be true for every reversible circular process, and the relation 



7jr = u (la.) 



f 



must hold good for every circular process which is in any way 

 possible. 



§ 2. Although the necessity of this proposition admits of 

 strict mathematical proof if we start from the fundamental prin- 

 ciple above quoted, it thereby nevertheless retains an abstract 

 form, in which it is difficultly embraced by the mind, and we 

 feel compelled to seek for the precise physical cause, of which 

 this proposition is a consequence. Moreover, since there is no 

 essential difference between internal and external work, we may 

 assume almost with certainty that a proposition which is so ge- 

 nerally applicable to external work cannot be restricted to this 

 alone, but that, where external work is combined with internal 

 work, it must be capable of application to the latter also. 



Considerations of this nature led me, in my first investigations 

 into the mechanical theory of heat, to assume a general law 

 respecting the dependence of the active force of heat on tempe- 



