82 M. R. Clausius on a modified Form of the second 



might assume this as known from my former memoirs or from 

 those of other authors, but to refer back would be inconvenient ; 

 and besides this, the demonstration I shall here give is prefer- 

 able to my former one, because it is at once more general and 

 more concise. 



Theorem of the equivalence of Heat and Work. 



Whenever a moving force generated by heat acts against an- 

 other force, and motion in the one direction or the other ensues, 

 positive work is performed by the one force at the same time that 

 negative work is done by the other. As this work has only to 

 be considered as a simple quantity in calculation, it is perfectly 

 arbitrary, in determining its sign, which of the tw^o forces is 

 chosen as the indicator. In researches which have a special 

 reference to the moving force of heat it is customary to deter- 

 mine the sign accordingly, by counting as positive the work done 

 by heat in overcoming any other force, and as negative the work 

 done by such other force. In this manner the theorem of the 

 equivalence of heat and work, which forms only a particular case 

 of the general relation between vis viva and mechanical work, 

 can be briefly enunciated thus : — 



Mechanical work may be transformed into heat, and conversely 

 heat into tvork, the magnitude of the one being always proportional 

 to that of the other. 



The forces which here enter into consideration may be divided 

 into two classes : those which the atoms of a body exert upon each 

 other, and which depend, of course, upon the nature of the body, 

 and those which arise from the foreign influences to which the 

 body may be exposed. According to these two classes of forces 

 which have to be overcome, I have divided the work done by 

 heat into internal and external work, which are subjected to essen- 

 tially different laws. 



With respect to the internal work, it is easy to see that when 

 a body, departing from its initial condition, suffers a series of 

 modifications and ultimately returns to its original state, the 

 quantities of internal work thereby produced must exactly can- 

 cel one another. For if any positive or negative quantity of in- 

 ternal work had remained, it must have produced an opposite 

 external quantity of work or a change in the existing quantity 

 of heat, and as the same process could be repeated any number 

 of times, it would be possible, according to the sign, either to 

 produce work or heat continually from nothing, or else to lose 

 work or heat continually, without obtaining any equivalent ; both 

 of which cases are universally allowed to be impossible. But if 

 at every retm-n of the body to its initial condition the quantity 

 of internal work is zero, it follows, further, that the internal work 



