﻿94 



Messrs. H. T. Tizard and D. B. Pye on the 



IV. It is now generally recognized that the rate of an 

 ordinary chemical reaction varies with the temperature in a 

 way which may be empirically expressed by an equation of 

 the form 



_B 



k=Ae T , (4) 



where k is the velocity constant, and A and B are constants, 

 B being the temperature coefficient. 



In the case of reactions evolving heat, we can write this : 



_B 



Q=A« T , (5) 



where Q is the initial rate of evolution of heat when a definite 



mixture is suddenly compressed to the temperature T. 

 the lowest ignition temperature T we have, 



B 



At 



Qo = A? 



(6) 



where Q can be measured from observation of the rate of 

 cooling of the gases at a temperature slightly below the 

 ignition point : i. e., 



Qo=«*.(T»-0), (7) 



where a is the cooling factor, c v the specific heat of the 

 mixture, and 6 the temperature of the walls. 



Now suppose that the gases are compressed initially to a 

 higher temperature T : the initial rate of loss of heat will 

 then be higher than Q , namely 



but since the effect of temperature on the rate of evolution 

 of heat due to the reaction is so much greater than that on 

 the rate of loss of heat, it is sufficiently accurate at present to 

 assume for our purposes a constant initial rate of loss of heat 

 = Q . The initial rate of reaction at the higher temperature 

 will be given by 



Q T = A<?~ 7E \ 

 From (5) and (6) we have 



^'ii 1 -^- • • • - (8) 



where b = 0*4343 B. 



Now under these circumstances the net rate of gain of heat 



is (Qt — Qo) calories per second. 



