Walker, The Poly tropic Curve 



Substituting- these values in (3) 



tq=i- rv~v — 7\ " " (4) 



a— I + ac(p — I) 



Given pressure limits are evidently conditioned by 



ar n — constant = C. 

 Given volume limits imply that r is constant. 

 Expression (4) now becomes 



A - tzl r + • tl* r » 



^- ~ (5) 



where A and B are constants 



A -lt 



B = c(i + op-i) 

 The cycle shown in Fig. 2 has already been investigated 

 in a previous article. 3 There it is shown that the efficiency 

 of this cvcle is given by an expression of the form 



A 1 -hr ' _ 



^ =I - b^W - - - - (6) 



where A 1 and B 1 are constants. 



The efficiency-compression ratio curves (i.e., y] against r) 

 for this second cycle, as derived from equation (6), are shown 

 by the full line curves of Fig. 3, for different values of p, where 

 also are shown the dotted curves giving the relationship 

 between yj and n as expressed by (5). 



For the purpose of showing these two sets of curves 

 together in a convenient way, it should be stated that the 

 compression ratio chosen as constant in (5) is taken as 14, a 

 figure integrally proportional to the value of n for adiabatic 

 compression, here assumed to be equal to 1.4. Further, the 

 maximum pressure in both cycles is fixed by the additional 

 assumption that a=i when 7=14 in (6). This limitation may 

 serve at the same time as an indication of the maximum 

 pressures permissible in practice, for if p 4 is the atmospheric 

 pressure, the resulting maximum pressure when 7=14 and 

 71=1.4 i s m tne neighbourhood of 500 lbs. per sq. in. abs. 

 Obviously, another result of the choice made is that the 

 limiting cases of the cycle of Fig. 1 when 7?, = o and 1.4 are also 

 the limiting cases of the cycle of Fig. 2 when r= 1 and 14. 

 This appears readily from an examination of the graphs in 

 Fig. 3 where the dotted and full lines represent the variation 



3. Engineering, "A New Thermodynamic Cycle," April 9, 1920. 



