Page:Scientific Papers of Josiah Willard Gibbs.djvu/206

170 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 rarefaction 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 $$G_{1}$$ and $$G_{2}$$ without condensation (i.e., when $$\beta_{1} + \beta_{2} = 1$$), it appears from equation (307) that the relation between $$m_{1}, m_{2}$$, 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 $$G_{1}$$ 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 $$G_{1}$$ and $$G_{2}$$, and also the pressure, 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 $$G_{3}$$ under constant pressure is attended with evolution of heat. If $$B = 0$$ (a case, as has been seen, of especial importance), the heat obtained by the formation of a unit of $$G_{3}$$ out of $$G_{1}$$ and $$G_{2}$$ without change of volume or of temperature will be equal to $$C$$. If this quantity is positive, and the total quantities of the gases $$G_{1}$$ 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 $$m_{1}$$ or of $$m_{2}$$, and for an infinite value of $$t$$ we shall have finite (neither infinitesimal 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