Fundamental Theorem in the Mechanical Theory of Heat, 97 



A transformation which thus remains at the conchision of 

 a circular process without another opposite one, and which 

 according to this theorem can only be positive, we shall, for 

 brevity, call an uncompensated transformation. 



The different kinds of operations giving rise to uncompensated 

 transformations are, as far as external appearances are concerned, 

 rather numerous, even though they may not differ very essen- 

 tially. One of the most frequently occurring examples is that 

 of the transmission of heat by mere conduction, when two bodies 

 of different temperatures are brought into immediate contact; 

 other cases are the production of heat by friction, and by an 

 electric current when overcoming the resistance due to imper- 

 fect conductibility, together with all cases where a force, in doing 

 mechanical work, has not to overcome an equal resistance, and 

 therefore produces a perceptible external motion, with more or 

 less velocity, the vis viva of which afterwards passes into heat. 

 An instance of the last kind may be seen when a vessel filled 

 with air is suddenly connected with an empty one ; a portion of 

 air is then propelled with great velocity into the empty vessel 

 and again comes to rest there. It is w^ell known that in this 

 case just as much heat is present in the whole mass of air after 

 expansion as before, even if differences have arisen in the several 

 parts, and therefore there is no heat permanently converted into 

 work. On the other hand, however, the air cannot again be 

 compressed into its former volume without a simultaneous con- 

 version of work into heat. 



The principle according to which the equivalence-values of 

 the uncompensated transformations thus produced are to be 

 determined, is evident from what has gone before, and I will 

 not here enter further into the treatment of particular cases. 



In conclusion, we must direct our attention to the function T, 

 which hitherto has been left quite undetermined ; we shall not 

 be able to determine it entirely without hypothesis, but by 

 means of a very probable hypothesis it will be possible so to do. 

 I refer to an accessory assumption already made in my former 

 memoir, to the effect that a permanent gas, when it expands at a 

 constant temperature, absorbs only so much heat as is consumed by 

 the external work thereby produced. This assumption has been 

 verified by the later experiments of Regnault, and in all proba- 

 bility is accurate for all gases to the same degree as Mariotte 

 and Gay-Lussac's law, so that for an ideal gas, for which the 

 latter law is perfectly accurate, the above assumption will also be 

 perfectly accurate. 



The external work done by a gas during an expansion dv, 

 provided it has to overcome a pressure equivalent to its total ex- 

 pansive force j9, is equal to pdv, and the quantity of heat absorbed 



Phil Mag, S. 4. Vol. 12. No. 77, Aug, 1856. H 



