THE DETONATION PROCESS 75 



and from Eqs. (3.2) and (3.3) 



Po, Vo being evaluated at the initial point and P, V on the R-H curves. From these 

 two equations, it is evident that investigation of the difference between D and 

 c + M is equivalent to determining the sign of the difference 



(3.8) VV - VKD - uy = (-|^)^ - ^^" 



at various points on the R-H curve. The adiabatic slope and slope of the R-H 

 curve at any point are related by the equation 



{ovJr \dv)s~^\ds)Xdv)R 



where the subscript R indicates differentiation along the R-H curve. Rearranging, 

 we have 



In order to analyze the two factors on the right we note that from thermodynamics 



(fX-(l-a 



which is a positive quantity, i.e., an adiabatic decrease in volume is accompanied by 

 a rise in temperature. (This fact is readily demonstrated from more familiar thermo- 

 dynamic quantities: specific heat, thermal expansion coefficient, adiabatic com- 

 pressibility.) From the first and second laws 



TdS = dE + PdV 

 and hence 



From the energy equation (3.6) for points on the R-H curve we obtain 



Sul:stituting for (dE/dV}R yields 



It is evident that the sign of ( dS/ dV)R depends on the relative slopes of the line join- 

 ing the initial and final states on the P-V diagram and the tangent to the R-H curve 

 at the point representing the final state. If the R-H curve is concave upward, as 



