82 THE DETONATION PROCESS 



periments. As H. Jones points out, the values of h required to fit this 

 type of data are not in very good agreement with other evidence and 

 are furthermore totally unreasonable for the front of detonation waves 

 as they lead to excluded molecular volumes greater than the total avail- 

 able volume. Jones (50) has therefore developed equations of state 

 along somewhat different lines in order to calculate detonation condi- 

 tions in solid explosives. At high pressure he fits an equation based on 

 theoretical results for the solid state to data of Bridgman and at lower 

 pressures employs a virial equation. The former equation Jones takes 

 to be of the form 



P = RTf 



(I-) 



dE, 



© 



<i) 



where Eo{V/N) is assumed to be the potential energy of interaction of 

 molecules in the gaseous product and N is the number of moles. The 

 internal energy Eo is expressed in the form 



Eo{V/N) = Ae--y/^ -f B{V/N) + C 



the first term representing repulsive forces, the second attractive forces. 

 In order to obtain suitable values of these constants, Jones considers 

 first the energy of normal modes of vibration of molecules in a solid, 

 assumed fully excited. With this interpretation, the function / can be 

 evaluated from compressibility data for gases under high compression, 

 and a constant value is found to be a good representation of Bridgman's 

 results for nitrogen at68°C.,6<P<15 kilobars. The assumed equa- 

 tion of state is then of the form 



P = aAe--v/^ - B + RTf 

 the constants found to fit Bridgman's data being 



/ = 0.313 cm.-*"^ A = 855 kcal./mole 



a = 0.263 cm.-3 B = 0.139 kcal./mole 



The constant C in the energy equation is taken to be —5.80 kcal./mole 

 to make the minimum energy equal to the heat of vaporization. At 

 lower temperatures a virial equation is used: 



^ = RT -\- bP + cP' + (IP' 



N 



