Rate of Explosion in Gases. 95 



If t is the normal temperature, and t the temperature of 

 the gas after explosion, 



mO v (t— 1 ) + energy at N.T. P. = energy of exploded gas ; 



LLX 771 



/. mC v (t-to) = h + ^tv-Voy—poV+poVo-; 



.-- iS ^ n - +t , (8) 



But p = mRf, 



Also, from equation (2), we get 



pv = !— T (v — v)v+p v ; 

 v o 



•' • 7T "! 7 > + ^-« (*> " V o) 2 - W + PoW^ i + mR«o 



= --2( v o-v)v+p v. . (4) 



This establishes a relation between V and v. The velocity 

 of a permanent explosion is therefore a function of the density 

 of the exploded gas. 



When an explosion starts its character and velocity are 

 continually changing until it becomes a wave permanent in 

 type and of uniform velocity. I think it is reasonable to 

 assume that this wave — i. e. the wave of which the velocity 

 has been measured by Prof. Dixon — is that steady wave 

 which possesses minimum velocity ; for, once it has become a 

 permanent wave with uniform velocity, no reason can be 

 discovered for its changing to another permanent wave 

 having a greater uniform velocity and a greater maximum 

 pressure. 



This particular velocity may be discovered by eliminating v 

 from the equations 



Y=f(v) 

 and dV 



dv 



It may be well to point out that under these circumstances 

 the entropy of the exploded gas is a maximum. This may be 

 easily shown thus : — 



