224 
Sec. G -13- Eq. 46-47 
where Q is the heat of reaction at constant_volume (heat absorbed) per M 
grams at the initial temperature T,, while C; is the mean heat capacity at 
constant volume of M grams of the burnt gases from T, to Tj. It should be 
noted that Q and C, are to be computed on the basis of the final composi- 
tion at T, not the composition at T 
(Bali iby 
Eq. (44) and (45) can be combined into an equation for determining Toy: 
2 Mp RTpi/Yoy = V+ Cy (Toy - 1). (46 )* 
If the reaction went quantitatively so that shifts of the equilibrium with 
temperature and pressure did not enter, this equation could be solved for 
Toy, @iven the dependence of G and ¥ on To;- However, in practice mp and Q 
depend indirectly on T,. because the equilibrium composition of the products 
depends on T,.. This complicates the calculations considerably but does not 
alter the principles involved. Having found T5;, one can compute D; from the 
following combination of Eq. (41) and (43): 
Dy = (Sait VD) Was RT; / ¥p3M ea)s 
b. Comparison with experiment. These methods have been applied to 
mixtures of hydrogen and oxygen by Lewis and Friauf1*, These authors chose 
for their calculations the best values available at that time for the heat 
capacities of the several substances involved. They are mostly four-constant 
empirical equations which could be somewhat improved with the modern data 
available. The resultant numerical changes in the results would be very 
Slight however. The data on the equilibria 2H, + Op 212 H50 and Th, = Ziel 
seem also to be reliable, but the equilibrium H,0 + 4 Op = 20H, which becomes 
important in mixtures rich in oxygen, cannot be calculated even at present 
with high precision because of the uncertainty in the heat of this reaction. 
The equilibrium 05 = 20 was not allowed for by the authors and they did not 
take into account the excess heat capacity of oxygen molecules due to 
electronic excitation. Both these omissions are not important. All in all 
it appears that similar calculations undertaken today with the aid of the 
most modern thermal data available would give results differing from those 
of Lewis and Friauf only insignificantly. 
The following Table 6-1. gives a comparison of the theory with the 
observations of Dixon and others on gases at atmospheric pressure and room 
temperature, confined in tubes of more than 20 mm, diameter. 
