122 PHENOMENA, ATOMS, AND MOLECULES 



A similar calculation ^^ for the oxy-hydrogen flame gives a temperature 

 of 3700 deg. K. and for the oxy-acetylene flame about 7000 deg. K. 

 Of course at such high temperatures as these the products of the com- 

 bustion would be largely dissociated so that the full heat of the reaction 

 would not be available, and the flame temperatures are therefore much 

 lower. For the case of the .atomic hydrogen flame we find 



(I -x) Ho= [2xCi-\~ (i -^) C2] T 



where T is the temperature of the flame and x the degree of dissociation 

 at this temperature; Ci and C2 are the mean specific heats of the atoms 

 and molecules, respectively. By trial, using the values of x from Table I, 

 we find that the equation is satisfied if we take T = 3990 deg. K. ; the 

 degree of dissociation, x, at this temperature is 0.62. Similar calculations 

 for the other flames, taking into account the degree of dissociation ^'^ of the 

 water vapor and carbon dioxide, give for the oxy-hydrogen flame 

 T = 3370 deg. K. and x = 0.20. For the oxy-acetylene flame T = 3750 

 deg., at which temperature the water vapor is about 38 per cent and the 

 carbon dioxide about 89 per cent dissociated. 



These temperatures for the oxy-hydrogen and oxy-acetylene flames 

 are still too high, since the hydrogen (and probably the oxygen) in the 

 partly dissociated products of combustion at these high temperatures must 

 be largely dissociated into atoms. The effect of this will be to increase the 

 degree of dissociation of the H2O and CO2 beyond that taken into account 

 in the calculation. An error of this kind, however, does not occur in the 

 calculation of the temperature of the atomic hydrogen flame. Thus the 

 calculations indicate that an atomic hydrogen flame is far hotter than either 

 the oxy-hydrogen or the oxy-acetylene flame. 



There is another factor which tends greatly to increase the temperature 

 of the atomic hydrogen flame even above the calculated value of 4000 deg. 

 The atomic hydrogen, instead of being originally at room temperature, 

 is already at a high temperature at the moment of its escape from the arc. 

 The conditions are analogous to those in an oxy-hydrogen flame in which 

 both gases are preheated. Thus the upper limit of temperature is fixed 

 only by the degree of dissociation of the hydrogen and the rate at which 

 heat is lost by radiation or contact with bodies of lower temperature. 



The fact that the degree of dissociation of hydrogen into atoms is very 

 much less at a given temperature than that of carbon dioxide into oxygen 

 and carbon monoxide is an important factor making the atomic hydrogen 

 flame much hotter than the oxy-acetylene flame. 



^° The specific heats for these calculations were taken from a table given on p. 80 

 of Lewis and Randall's "Thermodynamics." 



" Langmuir, Jour. Amer. Chem. Soc, 28, 1378 (1906). 



