80 THE DETONATION PROCESS 



Substituting in the energy equation (3.11) and using c^ = yPV we have 



iM ^' ~ ^^' V = Q + CAT - To) 

 Py 



Neglecting P^ in comparison to P^ and using the ideal gas law, this 

 becomes 



(3.12) h^^^^ = Q + CAT - To) 



7 



If, in the explosion of a mixture of gases, the distribution of atoms in 

 the molecular products were independent of temperature and pressure, 

 both Q and n could be evaluated on the basis of quantitative reaction, 

 and Eq. (3.12) could be solved for the final temperature T if the vari- 

 ation of 7 and Cv with T is known. Actually, of course, the equilibrium 

 constant of gaseous reactions depends on P and T. Furthermore, we 

 have no a priori assurance that either quantitative reaction or the equi- 

 librium condition is the one determining the state of the products at 

 the head of a detonation wave. It is therefore of interest to compare 

 results of both possible calculations with observed detonation veloci- 

 ties. Changes in equilibria affecting Q and n make the determination 

 of T from Eq. (3.12) much more tedious than if the equilibrium were 

 frozen, but Lewis and Friauf (67) have made such calculations for mix- 

 tures of oxygen and hydrogen with various excesses of both components 

 and for the stoichiometric mixture (2H2 + O2) with added inert gases. 

 The equilibria allowed for were 2H2 + 62 = H2O, H2 = 2H, 2H2O 

 + 02 = 40H, but not O2 = 20. Although the data used and assump- 

 tions made could be improved there is apparently no reason to believe 

 that the results are seriously in error. Reference should be made to 

 the original paper for further details. Once the final temperature T is 

 determined calculation of the detonation velocity D is made from the 

 equation 



tiRT 



,3,3, .4..=tj^-=„,„^^^, 



obtained from the approximate relation that 



Vo-V={P-Po)\-^- 



The calculations of Lewis and Friauf compared with experimental 

 data of Dixon (29) are copied in Table 3.1. It is seen that the equi- 



