September 24, 1908J 



NA TURE 



519 



Third Operation. — The piston returns, compressing tlic- 

 woriving fluid, but allowing the heat of compression to 

 escape, so that the temperature remains during the opera- 

 tion at its lowest point. 



Fourth Operation. — The piston compresses the worliing 

 fluid, without allowing any loss of heat, to such an extent 

 that the temperature rises again to its highest point, and 

 the working fluid exists at the end of this operation at 

 the same volume, pressure, and temperature as at the 

 beginning. 



This assumed series of operations would give a certain 

 available work area, the mdicated power ot the engine, 

 inasmuch as the work done by the working fluid would 

 be greater than that done upon it. If, however, it be 

 assumed that in all the operations the direction of motion 

 of the piston be reversed, then compression without loss 

 of heat would take place in the second operation ; further 

 compression, but with sufficient heat loss to keep tempera- 

 ture constant, would occur on the' first operation ; the 

 fourth operation would follow with expansion, and the 

 third operation would conclude also with expansion. The 

 engine would be reversed by beginning with the second 

 operation, moving the piston backwards in the order 

 second, first, fourth, third. Carnot shows that this reverse 

 operation would be performed by exactly the same amount 

 of work as was given out by the direct operation, and 

 that an amount of heat would be returned at the higher 

 temperature equal to that which was added in the first 

 case. 



.An engine which fulfils these conditions, Carnot states, 

 will give the greatest amount of work which can be 

 obtained from a given quantity of heat falling through a 

 given temperature range. And it is evident that this 

 must be so, because, if we assume the e.xistence of any 

 engine under the same conditions giving a greater amount 

 of work from the same heat, then that engine could drive 

 a Carnot engine in the reverse direction in such propor- 

 tion as to return to the higher temperature a greater 

 amount of heat than it abstracted, and so mechanical 

 energy could be obtained without any heat fall whatever. 

 This marvellous demonstration is obviously independent of 

 the nature of the working fluid ; it applies equally to all 

 working substances, whether solid, liquid, or gaseous, 

 whether physical state changes or not. It at once gives 

 a standard of the limit of mechanical power which could 

 possibly be obtained from a given amount of heat and a 

 given temperature fall. 



The Carnot cycle operations, as here given, are applic- 

 able either to the material or to the dynamical theory of 

 lieat ; but Carnot originally stated that the whole of the 

 heat added in the first operation was to be discharged in 

 the third. Under the material or caloric theorv, work 

 was supposed to be done by the fact of fall in tempera- 

 ture. Naturally, as the heat was material it could not 

 be destroyed or changed into mechanical energy. The 

 production of mechanical energy was supposed to be in- 

 cidental to the fall of temperature, much in the same way 

 as mechanical energy was produced by the fall of water- 

 level, and this analogy is used throughout Carnot's work 

 of 1824. 



Carnot thus succeeded in proposing a standard of 

 efficiency which was applicable to any heat engine, what- 

 ever the working fluid and whatever the operative cycle. 

 By his method a limit could be set, fixing the maximum 

 of mechanical energy to be obtained from a given heat 

 quantity and a given temperature range. To reduce this 

 to numerical values it was necessary, however, to experi- 

 ment on any one working fluid within the desired tempera- 

 ture range in order to determine the work area in its 

 relation to heat quantity and temperature fall. Carnot's 

 writings show that he intended to make such observa- 

 tions ; and, had he succeeded, thermodynamics would have 

 become a science at an early date. Carnot's death, how- 

 ever, in 1832, at the sadly early age of thirty-six years, 

 prevented this development. 



The name of Sadi Carnot will always be remembered by 

 mankind as the founder of one branch of the thermo- 

 dynamics of the heat engine. 



His vvork remained practically without notice for 

 thirteen years after his death, 'when, fortunatelv, it 

 attracted the attention of William Thomson during his 

 N'O. 2030, VOL. 78] 



attendance at the Laboratory of Regnault in the year 

 1845. Thomson was then twenty-one years of age, and 

 had already attained a considerable scientific reputation. 

 He took up the study of Carnot's work with enthusiasm. 

 He became Professor of Natural Philosophy in the Uni- 

 versity of Glasgow in 1846, and in 184S he read a Paper 

 before the Cambridge Philosophical Society " On an 

 Absolute Thermometric Scale founded on Carnot's Theory 

 of the Motive Power of Heat and calculated from Reg- 

 nault's Observations." Like Carnot, Thomson accepted 

 the " material " or " caloric " theory of the nature of 

 heat, although, like Carnot also, he had doubts as to its 

 truth. Assuming its truth, however, he carried Carnot's 

 reasoning much further, and deduced from the Carnot 

 cycle a thermometric scale which was absolute in the sense 

 that it defined the idea of temperature independently of 

 the properties of any particular body. 



It is very difficult to carry one's mind back to the 

 material theory of heat, but it is necessary to do so in 

 order to appreciate the rigid accuracy of the reasoning 

 of both Carnot and Thomson ; and it is especially desirable 

 to do so in order to understand the great step made in 

 this Paper. According to the " caloric " theory, heat was 

 supposed to be a subtle elastic fluid which permeated the 

 pores of bodies and filled the interstices between the mole- 

 cules of matter. The fundamental quality imagined of 

 this caloric or heat fluid was that of indestructibility and 

 uncreatability by any humanly controlled process. Bodies 

 became warmer when caloric was added to them, and 

 grew colder as it left them. Caloric, however, might be 

 added to a body without heating it. In this case the heat 

 was called "latent," and the state of the body changed 

 from solid to liquid or from liquid to vapour or gas. 



Caloric, too, was required in greater quantities for some 

 substances than others in order to warm the body equally. 

 The capacity for caloric was thus greater in some bodies 

 than in others. 



If any particular body were heated without change of 

 state it was hotter ; that is, its temperature rose when 

 the quantity of caloric present was increased. It was not 

 difficult to define equality of temperature. This was 

 defined by a constant condition when brought into contact. 

 But it was very difficult indeed to define temperature on 

 any rational scale. 



To the acute and brilliant inteUect of William Thomson 

 it became apparent that he had in the Carnot cycle a 

 pow^erful instrument capable of widely general use, apart 

 altogether from the theory of heat engines ; and he here 

 uses it in a most skilful way to give definiteness and 

 universal application to the idea of temperature, as Prof. 

 Larmor states, " elevating the idea of temperature from 

 a mere featureless record or comparison of thermometers 

 into a general principle of physical nature." 



Thomson accordingly defines equal differences of tempera- 

 ture in terms of the reversible or Carnot engine. 



Equal temperature differences are to be differences 

 between the temperatures of the source of heat and the 

 refrigerator, when the proportion of work produced from 

 a given quantity of heat is the same. Thermometers 

 graduated in degrees calculated in this way could naturally 

 be treated as instruments based on definite principles, in- 

 dependently of any properties of any particular material. 

 The idea of temperature here was in rigid logical con- 

 sistency with the " caloric " theory of heat, and it carried 

 out completely the analogy between power derived from 

 the same quantity of heat falling from a higher to a lower 

 level, and resembling a fall of water in producing its 

 effects. For equal quantities of " caloric," as of " water," 

 temperature fall was regarded as similar to fall in space, 

 and so an accurate idea of the nature of temperature 

 difference is attained. 



This definition, however, gave a scale greatly differing 

 from that of mercurial, air, and other thermometers, the 

 degrees defined by it corresponding to larger and larger 

 intervals on the air thermometer as temperature increases: 

 Prof. Tait pointed out also that on such a scale the 

 temperature of a body totally deprived of heat is negative- 

 infinite. 



All these difficulties do not detract from the fundamental 

 importance of the idea here enunciated for the first time : 

 the idea of an absolute thermometric scale theoretically 



