170 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



of dissipated energy. Thus, if we regard a mixture of hydrogen 

 oxygen, and vapor of water as an ideal gas-mixture, for a mixture 

 containing any given quantities of these three gases at any given 

 temperature there will be a certain volume at which the mixture will be 

 in a state of dissipated energy. In such a state no such phenomenon 

 as explosion will be possible, and no formation of water by the action 

 of platinum. (If the mass should be expanded beyond this volume, 

 the only possible action of a catalytic agent would be to resolve the 

 water into its components.) It may indeed be true that at ordinary 

 temperatures, except when the quantity either of hydrogen or of 

 oxygen is very small compared with the quantity of water, the state 

 of dissipated energy is one of such extreme rarefaction as to lie 

 entirely beyond our power of experimental verification. It is also to 

 be noticed that a state of great rarefaction is so unfavorable to any 

 condensation of the gases, that it is quite probable that the catalytic 

 action of platinum may cease entirely at a degree of rarefaction far 

 short of what is necessary for a state of dissipated energy. But with 

 respect to the theoretical demonstration, such states of great rarefac- 

 tion are precisely those to which we should suppose that the laws of 

 ideal gas-mixtures would apply most perfectly. 



But when the compound gas G 3 is formed of G-^ and G 2 without 

 condensation (i.e., when ^+^ = 1), it appears from equation (307) 

 that the relation between m lt m 2 , and m 3 which is necessary for a 

 phase of dissipated energy is determined by the temperature alone. 



In any case, if we regard the total quantities of the gases 6^ and 

 G 2 (as determined by the ultimate analysis of the gas-mixture), and 

 also the volume, as constant, the quantities of these gases which 

 appear uncombined in a phase of dissipated energy will increase with 

 the temperature, if the formation of the compound G 3 without 

 change of volume is attended with evolution of heat. Also, if we 

 regard the total quantities of the gases G and G 2 , and also the 

 pressure, as constant, the quantities of these gases which appear un- 

 combined in a phase of dissipated energy, will increase with the 

 temperature, if the formation of the compound G 3 under constant 

 pressure is attended with evolution of heat. If B = Q (a case, as 

 has been seen, of especial importance), the heat obtained by the 

 formation of a unit of G 3 out of G l and G 2 without change of volume 

 or of temperature will be equal to G. If this quantity is positive, 

 and the total quantities of the gases G l and G 2 and also the volume 

 have given finite values, for an infinitesimal value of t we shall have 

 (for a phase of dissipated energy) an infinitesimal value either of ^ 

 or of m 2 , and for an infinite value of t we shall have finite (neither in- 

 finitesimal nor infinite) values of m 1 , m 2 , and m 3 . But if we suppose 

 the pressure instead of the volume to have a given finite value (with 



