394 



SCIENCE. 



[N. S. Vol. XVI. No. 401. 



by ordinary tides are safe, and so are all those 

 low enough to be attractive to iiddler crabs. 



Areas covered by the monthly high tides are 

 safe, except in midsummer if it has been dry 

 enough to kill out the young fish and has then 

 rained enough to fill the low places. The 

 danger points are such as I pointed out in 

 Science and more at length, recently, in 

 Special Bulletin T of the New Jersey Agri- 

 cultural College Experiment Station. 



John B. Smith. 



Rutgers College, 

 August 20, 1902. 



' LATENT HEAT ' AND THE VAPOE-ENGINE CYCLE. 



The discussion, some time since published 

 in Science, relating to the vapor-engines, so- 

 called, and the ' latent heat fallacy ' led to in- 

 quiries from various sources regarding the 

 exact distribution of the work of thermo- 

 dynamic transformation in the case of the 

 steam, and other vapor-engines. The follow- 

 ing may perhaps make clearer the relation be- 

 tween the action of sensible and of ' latent ' 

 heat in such cycles. The discussion of this 

 problem has been one of the annual topics in 

 the classes of the writer for years past. 



The usual standard form of engine-cycle, in 

 all departments of applied thermodynamics 

 and with the steam, and other vapor-engines 

 employed in the industries, is that known as 

 the Rankine cycle with incomplete expansion, 

 as in the figure. It consists of a line of con- 

 stant maximum pressure, an adiabatic expan- 

 sion-line, as nearly as practicable, a line of con- 

 stant volume, a line of constant minimum 

 pressure, and the cycle is closed by a line of 

 constant volume. Assuming unit-weight of the 

 working substance to be carried through such a 

 cycle, it is easy, by the adoption of one of 

 Rankine's beautifully ingenious mathematical 

 devices, to obtain the following expression for 

 work of one cycle in which p, T and u are the 

 pressures, the temperatvires, absolute, and the 

 specific volume of the charge; H is the latent 

 heat of vaporization and J is Joiile's factor. 

 The subscripts indicate, respectively, values of 

 p and T on the expansion line and of p on the 

 back-pressure line : 



ABODE— AFG + ABCFA + CDEO 

 = (i.) -f(n.) -f(ni.) 



U=J[T,-T,(I+hg.TJT,)] 



+ ir,('J\- T,)IT, + {p,-2h)«2- 



The three parts into which the measure of 

 net work, U, divides itself are obviously a func- 

 tion of temperature which measures the effect 

 of the thermodynamic application of sensible 

 heat, a function of temperature and ' latent ' 

 heat which is instantly recognized as the meas- 

 ure of the Carnot efficiency of the ' perfect en- 

 gine,' and a function of the terminal and back 

 pressures and specific volume of the charge at 

 the minimum temperature of the expansion- 

 line. This latter is obviously, ■ also, the work 

 between the terminal and back-pressures, the 

 rectangle, CDEG. The intermediate term is 

 the work obtainable from the same quantity of 

 fluid between the same two temperatures, T, 

 and T„ in the Carnot cycle, ABCFA, and it is 

 thus evident that the first term must measure 

 the remaining area of the Rankine cycle, the 

 triangle, AFG; which is as evidently the work 

 alike of the compression in the Carnot cycle 

 and that of expansion of unit weight of a mix- 

 ture of steam and its liquid between the state' 

 of liquid at maximum temperature at A and 

 that of mixed vapor and liquid at the lower 

 limit of expansion pressure and temperature, 

 p, and T,. 



Noting the proportions of the areas thus 

 measiu-ed, it is seen that, with any fixed value 

 of the latent heat of vaporization, the last- 

 named quantity has a lower relative measure 

 as the ratio of expansion and the temperature- 

 range decrease, and, vice versa, that the quan- 

 tity of work performed within the same tem- 

 perature-range is in all cases greater in the- 

 Rankine than in the perfect engine cycle by 

 this amount; that the work in either cycle is 

 proportional, in some direct measure, to the 

 quantity of the heat of vaporization; that the 

 heat entering the fluid during vaporization is 

 all converted into work and that none is em- 

 ployed to change temperature and thus to be- 

 come stored as sensible heat. Observing, also,- 

 that the Carnot cycle is that of maximum effi- 

 ciency, it follows that the work measured by 

 the first term, and by AFG, is obtained at a 

 comparative loss of efficiency and that, there- 

 fore, the work gained in the Rankine cycle,. 



