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PHYSICS: A. G. WEBSTER 
ON THE POSSIBLE FORM OF THE EQUATION OF STATE OF 
POWDER GASES 
By a. G. Webster 
Ballistic Institute, Clark University, Worcester, Massachusetts* 
Communicated May 14, 1919 
It has been customary for ballisticians to make use of the equation proposed 
by Clausius, 
(1) 
in the simplified form, suitable for the high temperatures concerned, 
p (v - a) = RT. (2) 
At the same time it is customary to make use of the . experimental results of 
Mallard and le Chatelier and of Berthelot and Vieille on the specific heats 
which state that C^, is a linear increasing function of the temperature. While 
apparently no experiments have been made on Cp it is assumed that the dif- 
ference of the specific heats is constant, as in the case of an ideal gas. 
It has occurred to me to examine the question of the most general form 
possible for the equation of state that shall permit of variability of the 
specific heats, but maintain the constancy of their difference. This question 
does not appear to have been treated, 
By an application of the two laws of thermodynamics we obtain the well- 
known equation 
(C,-Q^^=r. (3) 
dp dv 
If we use the usual letters for differential equations, putting x for v, y for p, 
z for T divided by Cp — C^, supposed constant, and as usual p for dz/dx, q 
for dz/dy we have the very simple partial differential equation, 
F = pq-z = 0. (4) 
This may be very simply integrated by Cauchy's method, which consists in 
integrating the system 
dx _dy _ dz dp _ _ dq _du 
P ~Q~ PpTOq' X + pZ~ YTqZ~~^' 
where the capital letters represent the derivatives of F with respect to the 
corresponding small letters, and u is an extraneous parameter. Having found 
* Contribution from the Ballistic Institute, Clark University, No. 5. 
