CONTRIBUTIONS FROM THE JEFFERSON RHYSICAL LABORATORY, 

 HARVARD UNIVEliSITY. 



A PQ PLANE FOR THERMODYNAMIC CYCLIC 

 ANALYSIS. 



By IIarvky N. Davis. 



Presented by John Trowbridge, December 14, 1904. Received January 9, 1905. 



Four years ago, Dr. C. E. Lucke pointed out in an admirable paper* 

 the value of what he calls a "cyclic analysis of heat engines." The 

 variety of processes which are available when the working substance is 

 a gas rather than a vaporized liquid is so great, and the influence of the 

 nature and dimensions of a given cycle, not only upon its efficiency, but 

 upon many other properties, is so complicated, that it is evidently both 

 interesting and important to make a purely theoretical study of cycles 

 as such, and to endeavor to obtain statements of the questions involved 

 in terms of the cycles themselves. And for this purpose, the best meth- 

 ods will almost always be graphical ones, as these are at once the most 

 powerful in investigation and the clearest in exposition. It is desired, 

 in this paper, to reiterate Dr. Lucke's insistence on the value of work of 

 this kind, and to develop a method which shall be more general, and 

 therefore more fruitful, than the one-dimensional graphics which he has 

 proposed. 



It is best to begin by inquiring how much must be given to determine 

 completely a cycle of a given type. If the cycle is to be represented on 

 the ordinary p v plane of thermodynamics, both its dimensions and its 

 position in the plane must be known. To describe its position will al- 

 ways require two coordinates, and it will be convenient to take for these 

 the pressure (P^) and the temperature {T^ of the working substance at 

 the beginning of the cycle, since these quantities are easily measured ; 

 often they are simply the pressure and temperature of the earth's at- 

 mosphere at the time, and so are not controllable, and for this reason it 

 is best to regard them, not as variables, but as parameters in the equa- 



* " A Method of Cyclic Analysis of Heat Engines," by Charles E. Lucke. The 

 School of Mines Quarterly, 22 [1901], pp. 223, 329, 411. 



