Prof. Thomson on the Dynamical Theory of Heat. 13 



It is impossible, by means of inanimate material agency, to de- 

 rive mechanical effect from any portion of matter by cooling it 

 below the temperature of the coldest of the surrounding objects'^. 



13. To demonstrate the second proposition, let A and B be 

 two thermo-dynamic engines, of which B satisfies the conditions 

 expressed in the enunciation ; and let, if possible, A derive more 

 work from a given quantity of heat than B, when their sources 

 and refrigerators are at the same temperatures, respectively . Then 

 on account of the condition of complete reversibility in all its 

 operations which it fulfills, B may be worked backwards, and 

 made to restore any quantity of heat to its source, by the expen- 

 diture of the amount of work which, by its forward action, it 

 would derive from the same quantity of heat. If, therefore, B 

 be worked backwards, and made to restore to the som'ce of A 

 (which we may suppose to be adjustable to the engine B) as 

 much heat as has been drawn from it during a certain period of 

 the working of A, a smaller amormt of work will be spent thus 

 than was gained by the working of A. Hence, if such a series 

 of operations of A forwards and of B backwards be continued, 

 either alternately or simultaneously, there will result a continued 

 production of work without any continued abstraction of heat 

 from the source ; and, by Prop. I., it follows that there must be 

 more heat abstracted from the refrigerator by the working of B 

 backwards than is deposited in it by A. Now it is obvious that 

 A might be made to spend part of its work in working B back- 

 wards, and the whole might be made self-acting. Also, there 

 being no heat either taken from or given to the source on the 

 whole, all the surrounding bodies and space except the refrige- 

 rator might, without interfering with any of the conditions which 

 have been assumed, be made of the same temperature as the 

 source, whatever that may be. AVe should thus have a self-acting 

 machine, capable of drawing heat constantly from a body sur- 

 rounded by others at a higher temperature, and converting it 

 into mechanical effect. But this is contrary to the axiom, and 

 therefore we conclude that the hypothesis that A derives more 

 mechanical effect from the same quantity of heat drawn from the 

 source than B, is false. Hence no engine wliatever, with source 

 and refrigerator at the same temperatures, can get more work 

 from a given qiumtity of heat introduced than any engine which 

 satisfies the condition of reversibility, which was to be proved. 



14. This proj)osition was first enunciated by Carnot, being 

 the expression of his criterion of a perfect thermo-dynamic en- 



* If this axiom be denied for all temperatures, it would have to be ad- 

 mitted that a self-actin}^ machine might be set to work and ])roduce me- 

 chanical effect by coolinf^ the sea or earth, with no limit but the total loss 

 of heat from the earth und sea, or, in reality, from the whole material world. 



