208 Prof. Clausius on the Internal Work 



different temperatures, — in the case of reversible alterations of 

 condition it can be brought about only by heat being converted 

 into work at the one temperature, and work back again into heat 

 at the other ; it is therefore already comprised among the trans- 

 formations of the first kind. And, as I have mentioned in my 

 previous memoir, we may in all cases regard a transformation of 

 the second kind as a combination of two transformations of the 

 first kind. 



We will now return to equation (II.), namely, 



j*^ + f ( IZ=0. 



dll is here the increment received by the quantity of heat pre- 

 sent in the body during an infinitely small change of condition, 

 and dQ is the quantity of heat simultaneously given up to ex- 

 ternal bodies. The sum dQ + dH is therefore the quantity of 

 heat which, supposing it to be positive, is freshly produced from 

 work, or if it is negative, must be converted into work. Accord- 

 ingly, the first integral in the above equation is the equivalent 

 value of all the transformations which have occurred of the first 

 kind ; the second integral represents the transformations of the 

 third kind ; and the sum of all these transformations must be, 

 as is expressed by the equation, equal to nothing. 



Hence, in so far as it regards reversible alterations of condition, 

 the theorem may be expressed in the following form : — 



If the equivalent value -^ be assumed for the production of the 



quantity of heat Q from work at the temperature T, a magnitude 

 admits of being introduced, as the second transformation correspond- 

 ing thereto, which has relation to the alterations of the condition 

 of the bodijy and is completely determined by the initial and final 

 conditions of the body, and which fulfils the condition that in every 

 reversible alteration of condition the algebraic sum of the transfor- 

 mations is equal to nothing. 



§ 11. We must now examine the manner in which the fore- 

 going theorem is modified when we give up the condition that 

 all alterations of condition are to take place reversibly. 



From what has been said in § 4 concerning non-reversible 

 alterations of condition, it is easy to perceive that the following 

 must be the general behaviour of all three kinds of transforma- 

 tions. A negative transformation can never occur without a 

 simultaneous positive transformation whose equivalent value is 

 at least as great ; on the other hand, positive transformations are 

 not necessarily accompanied by negative transformations of equal 

 value, but may take place in conjunction with smaller negative 

 transformations, or even without any at all. 



