Manchester Memoirs, Vol. Ixv. (1921), No. 2 



II.— The Polytropic Curve and Its Relation to 

 Thermodynamic Efficiency. 

 (With Note on the Uniflow Engine). 



By W. J. Walker, Ph.D., B.Sc, A.M.Inst.C.E., 



Lecturer in Mechanical Engineering in the College of 

 Technology, Manchester. 



(Received June 24th, 1920. Bead November 2nd, 1920.) 



Introduction. The writer's interest in this subject began 

 when engaged on a theoretical enquiry into the efficiency of 

 an Otto cycle gas engine as affected by water injection 1 during 

 the compression stroke. Since that time the opportunity of 

 carrying out experimental work on the subject has presented 

 itself. From these experiments, an account of which it is 

 hoped will be published at an early date, it appears that water 

 injection (no matter at what portion or during what period 

 of the engine cycle injection takes place) does undoubtedly 

 diminish the efficiency, although to a slight extent only. The 

 physical interest in the problem, however, lies in asking why 

 this should be so. 



The polytropic system of curves is defined as ' ' that system 

 representing the relation between any two of the quantities, 

 pressure, volume, or temperature of a gas, when the quantity 

 of heat supplied to or withdrawn from the gas is directly 

 proportional to the change of temperature." 



Thus if 



dQ = kdT ----- (1) 



where k is some constant, the corresponding mathematical 

 relationship between pressure and volume is readily obtained 

 and is as follows : — 



pv n = constant - - - - (2) 



k — Ay 



where n is constant and equal to 7 — w^ K p and K v being 



the specific heats of the gas at constant pressure and constant 

 volume respectively. 



1. " Internal Combustion Engineering," June 10th, 1914. 

 June 28th, IQ2I. 



