380 



SCIENCE. 



[N. S. Vol. XV. No. 375. 



tion has thus great intrinsic advantage 

 over the vapor of water as a working fluid 

 in the heat-engine. This is a well-known 

 and oft-repeated fallacy, and it has been 

 almost as common among inventors or 

 would-be inventors as was formerly, ac- 

 cording to Dircks, that of a ' perpetuum 

 mobile.' 



The thermodynamic efficiency of any 

 heat-engine is determined, at best, by the 

 range of temperature worked through and 

 without regard to the nature of its work- 

 ing substance. It is true that the practi- 

 cability of employment of one or another 

 fluid in the heat-engine varies with the 

 temperature- and pressure-ranges and that 

 there is as yet no known fluid which pre- 

 cisely adapts itself to the demand of the 

 engineer within the practical limits of 

 pressure and of temperature, coincidently, 

 which lie now safely, conveniently and 

 economically handles. He finds one fluid 

 suited to the pressure, the other to 

 the temperature-range, one to the upper, 

 another to the lower, portion of either 

 scale; but he knows of none which meets 

 his needs on both scales. 



The proposition regarding ' latent ' heats 

 is easily verified by reference to the well- 

 known expression of Rankine for the work, 

 Z7i, of the common vapor-engine cycle with 

 complete, adiabatic, expansion between T^ 

 and T,, and without compression:* 



U^ = J\dp = J""(JC'log, T^IT, + J); dp,l(H\)dT; 



= JC[T,-T,{1 + log,T,IT,)-\+ H,{T,-T,)IT,- 



where E^ is the ' latent ' heat of vaporiza- 

 tion at Tj in dynamic units. 



The work of compression in the Carnot 

 cycle, to which this cycle is reduced by its 

 introduction, is found by making H,=0, 

 the compression reducing the fluid to the 



•'Manual of the Steam- Engine,' p. 387. 



liquid state at the close of the compression 

 period, when we shall have 



Judp - 

 P2 



:JClT,-T,{l + \og,T,IT,)l 



Deducting this quantity, the first expres- 

 sion reduces to that for the work of the 

 Carnot cycle for vapors, 



U,-U, = II,{T,-T,)I1\; 



which is identical with that for gases when, 

 for H^, the latent heat of vaporization, is 

 substituted the latent heat of isothermal 

 expansion at T\* 



In other words, in the ' perfect-engine 

 cycle ' of Carnot, whether for one or an- 

 other working fluid, or even for solids 

 serving as working substances, the work 

 is all performed by ' latent ' heat ; while, 

 in the common steam-engine or other 

 vapor-engine cycle, it is obtained from 

 ' latent ' heat more and more completely as 

 the cycle approximates more and more 

 closely to the conditions of maximum effi- 

 ciency. 



It is further evident from the above 

 that efficiency is independent of the mag- 

 nitude of the value of E, in the Carnot 

 cycle, as well as of the measure of J or of 

 C, the specific heat. As Carnot himself 

 announced in 1824, maximum efficiency is 

 not dependent upon the nature of the 

 working fluid, and one vapor is as good as 

 another in this respect. The magnitude 

 of E determines how much heat shall be 

 stored in the working substance in each 

 cycle and how many units of weight of 

 that fluid will be required per unit of work 

 performed. Thus, with steam, a smaller 

 number of pounds per horse-power-hour 

 are required, other things equal, than with 

 ether, or, in fact, with any other known 

 substance ; although the number of thermal 

 units per unit of work developed in the 



* Thurston's ' Manual of the Steam- Engine/ 

 Vol. I., p. 796. 



