816 TRANSACTIONS OF SECTION G. 



The Jouie and Carnot laws are now known as the first and second laws dt 

 thermodynamics. 



The second law, in modern form, may be thus stated :^ 



Although heat and work are mutually convertible and in definite and invari- 

 able proportions, yet no conceivable heat engine is able to convert all the heat 

 given to it into work. Apart altogether from practical limitations, a certain 

 portion of the heat must be passed from the hot body to the cold body in order 

 that the remainder may assume the form of mechanical energy. 



The proportion of the total heat convertible into mechanical enei'gy depends 

 on the absolute temperatures of the hot and cold bodies ; it is unity minus the 

 lower absolute temperature upon the upper absolute temperature. 



It appears that during Thomson's struggle to reconcile the two apparently 

 opposing laws, Clausius, who had seen the same difficulty, arrived independently 

 at its solution and published a paper, ' On the Motive Power of Heat and the Laws 

 of Heat which may be deduced therefrom,' at the Berlin Academy in February 

 1850. In this paper, Clausius discusses Thomson's difficulties, and also arrives at 

 the conclusion that the Carnot cycle may be reconciled to Joule's law by the 

 omission of the supposition that during the third process the same amount of heat 

 is discharged from the cool body as was taken in from the hot one. He states : — 



' On a nearer view of the case we find that the new theories were opposed 

 not to the real fundamental principle of Carnot, but to the addition that no heac 

 is lost. For it is quite possible that in the production of work both may take 

 place at the same time : a certain portion of heat may be consumed and a further 

 portion transmitted from a warm body to a cold one ; and both portions may 

 stand in a certain definite relation to the quantity of work produced. This will 

 be made plainer as we proceed ; and it will be moreover shown that the inference 

 to be drawn from both assumptions may not only exist together, but that they 

 may mutually support each other.' 



In his 1851 paper, Thomson gives Clausius full credit for solving the difficulty 

 between the Carnot and the Joule principles. Thomson gives Clausius the full 

 credit for priority, but states that he was working on the same problem and had 

 arrived at the same solution in the year 1850, before he had seen Clausius' work. 

 Clausius, however, assumed the theory of a permanent gas, which required the 

 absence of joternal work, but Thomson was not prepared to assume this without 

 experiment. This determination rigidly to prove every necessary assumption, 

 and his clear conception of the points necessary for proof, led to the extensive 

 series of researches undertaken by Thomson and Joule with the object of deter- 

 mining how much gas thermometers differ from an absolute scale as determined 

 by the combination of the Joule and Carnot laws. 



liankine, as early as 1819, arrived at the general equation of thermodynamics 

 which expresses the relation between heat and mechanical energy, and indicated the 

 result of his investigations to the lloyal Society of Edinburgh in February 1850, 

 liankine thus arrived independently at the same result as Clausius about the same 

 time. Both Kankine and Clausius, however, adopted certain theories as to the 

 molecular structures and motions of gases, and their demonstrations to some 

 extent depended upon their theories. To Thomson and Joule we are deeply 

 indebted for the rigid proof of the two laws and for the rigid deduction of the 

 modern scale of temperature and the determination of absolute zero in its modern 

 form. Thomson now thus defines temperature: — • 



'The temperatures of two bodies are proportional to the quantities of heat 

 respectively taken in and given out in loc-alities at one temperature and at the 

 other respectively, by a material system subjected to a complete cycle of perfectly 

 reversible thermodynamic operations, and not allowed to part with or take in 

 heat at any other temperature; or, the absolute values of two temperatures are to 

 one another in the proportion of the heat taken in to the heat rejected in a perfect 

 thermodynamic engine, working with a source and refrigerator at the higher and 

 lower of the temperatures respectively.' 



