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XIX. Thermodynamic Cycles with Variable Specific Heat of 

 Working Substance. By Wm. J. Walker, B.Sc, School 

 of Technology, Manchester*. 



Summaey. — The paper deals with those thermodynamic cycles 

 which are of particular interest in internal combustion engineering 

 science. Approximate expressions for the efficiencies of the Con- 

 stant Volume and Constant Pressure Cycles, assuming variable 

 specific heat, have been obtained by other writers. In the present 

 paper the expressions for these efficiencies have been cast in 

 another and simpler form by first obtaining the general expression 

 for the efficiency of the Dual Combustion Cycle and then deducing 

 the efficiency expressions from that, for the Constant Volume and 

 Constant Pressure Cycles as particular cases. In conclusion, an 

 interesting relationship is pointed out between the efficiency ex- 

 pressions for these cycles as given, and that for the Carnot or 

 Constant Temperature Cycle. 



fl^HE following notes represent an attempt to obtain some 

 _L simple expression for thermal efficiency, involving 

 variable specific heat, which might be used as a standard 

 of comparison in estimating the relative performances of 

 internal combustion engines operating on different thermo- 

 dynamic cycles. Although thus primarily intended for 

 practical application, it is hoped that the results obtained are 

 of sufficient interest from the physical and theoretical stand- 

 points to warrant their being given here. 



Expressions for these efficiencies have already been ob- 

 tained by Wimperisf and Lees J for the Constant Volume 

 Combustion and Constant - Pressure Combustion Cycles 

 respectively. The method of analysis adopted here is an 

 extension of that applied by Lees. 



The general expression for the efficiency of the thermo- 

 dynamic cycle illustrated in fig. 1 will first be derived. 

 This type of cycle is typified by that on which the Blackstone 

 oil-engine is operated, and is here called the Dual Com- 

 bustion Cycle, some of the heat being imparted to the working- 

 fluid at constant volume and the remainder at constant 



* Communicated by the Author. 



t ' The Internal Combustion Engine,' p. 81, by H. E. Wimperis. 



X ' Engineering/ Jan. 1st, 1915. 



