August 20, 1920] 



SCIENCE 



175 



sity of Amsterdam, has been appointed pro- 

 fessor of mathematics; Professor E. von 

 Mises, of the Dresden technical school, has 

 been appointed professor of applied mathe- 

 matics, and Dr. Issai Schur has been promoted 

 to a full professorship of mathematics. Pro- 

 fessor C. Caratheodory has resigned, to accept 

 a professorship at the National University of 

 Athens. 



DISCUSSION AND CORRESPONDENCE 



EFFICIENCY IN THERMAL CALCULATIONS 



There is something- wrong with the com- 

 monly accepted definitions used in calcula- 

 ting efficiency when applied to thermal phe- 

 nomena. 



Take the following case as an example. An 

 ice-making machine is placed in a room that 

 requires heating. Let us calculate the effi- 

 ciency of the operation of heating the room. 

 Assuming the machine to be operated by an 

 electric motor, the heat supplied to the room 

 consists of two parts, the heat equivalent of 

 the electric current, and the heat withdrawn 

 from the water in making ice. As the entire 

 machine is located in the room, there are no 

 losses, all friction being utilized as useful 

 heat. We therefore have a case where the 

 useful heat is greater than the heat we paid 

 for, or an efficiency of over 100 per cent. 



For another illustration, consider the heat- 

 ing of a room by an electric heater. The 

 efficiency is 100 per cent., as all the energy 

 of the current goes into the room. But this 

 same current could have been used to run 

 machinery in the room, such as fans, sewing 

 machines, etc., that would have returned all 

 the heat to the room eventually. Should not 

 this additional work be considered in calcu- 

 lating the efficiency of the outfit? 



There is one long established law that gives 

 the clue to more suitable defiLnitions of 

 thermal heat units. Carnot established the 

 fact that the efficiency of an ideal heat engine 

 was equal to (T^ — T^)/T^ where T^ equals 

 the absolute temperature of the source of heat 

 and r, the temperature of the exliaust. In 

 other words the work that it is possible to 

 obtain from heat depends upon the difference 



in temperature as well as upon the calories 

 present. 



Our efficiency terms would be of more prac- 

 tical value if instead of using the calories we 

 should use a modified heat unit consisting of 

 the calory multiplied by the ratio referred to 

 above, taking the value T„ as the lowest tem- 

 perature of the surrounding air, condenser 

 water, etc. 



This would, of course, increase the mathe- 

 matical difficulties, but why say that a boiler 

 has an efficiency of 80 per cent, when but one 

 third of that 80 per cent, can be used by an 

 ideal engine. This method would also bring 

 out forcibly the tremendous losses in heating 

 houses by coal, without making use of the 

 power as a by-product. The inefficiency of 

 the steam locomotive is frequently commented 

 upon, but the inefficiency of raising the tem- 

 perature of a house 10° F. is so much greater 

 that it should be made evident to all. 



There is one serious objection to the use of 

 a ratio such as that of Carnot's cycle as part 

 of a unit of heat. That is, is Carnot's cycle 

 the best possible cycle? None other has been 

 developed as yet, but we have not established 

 the proposition that none can be developed. 



Allan W. Forbes 

 Worcester, Mass. 



In Mr. Forbes's interesting communication, 

 which the editor has been good enought to let 

 me see, he has perhaps overlooked the fact 

 that in a reversible cycle, the efficiency being 

 defined as the ratio of work done to heat 

 taken in for a motor, always less than unity, 

 if the efficiency of a freezing machine or 

 heating plant be defined as the ratio of heat 

 taken up to work done, this will be the recip- 

 rocal of the efficiency of the motor, and con- 

 sequently greater than unity. Evidently the 

 efficiency will be greater the smaller the tem- 

 perature interval to be covered. This was 

 pointed out many years ago by Lord Kelvin, 

 who called attention to the enormous waste in 

 heating a house, the difference of temperature 

 employed being that from the red heat of 

 combustion of the coal to the temperature 

 desired, when all that is needed is the small 



