Physical significance of entropy or of the second law

by Joseph Frederic Klein

as given by Eq. (33) for the instant, constitutes the driving motive which urges the gas toward thermal equilibrium. A similar difference or driving motive is the underlying impelling cause of all natural phenomena.

OF THE DIFFUSION OF GASES

This case of an irreversible process comes under group d. Concerning this phenomenon J. W. GIBBS established the following proposition:

"The entropy of a mixture of gases is the sum of the entropies which the individual gases would have, if each at the same temperature occupied a volume equal to the total volume of the mixture."

That the total entropy will be larger as a result of the mixing detailed under d, [p. 73], may be inferred from the following consideration: When two gases are thus brought together, it is more probable that in any part of the total space available for this mixture there will be found both kinds of molecules than only one kind of these molecules.

But this irreversible process can be explained in a more distinctly physical way. The two gases are originally at the same pressure and temperature; they mix without other changes occurring in surrounding bodies; the mixture (when diffusion is completed) is at the same pressure and temperature as the original gaseous constituents. Considering each gas by itself, what has happened as the result of diffusion is that each gas in its final state occupies a larger volume than in its initial, unmixed, state. The presence of the other gas in the mixture in no wise changes this fact. Of course this increment in volume is accompanied by a corresponding decrement in its pressure, without change in temperature. A sort of isothermal change of state has taken place in the passage from one condition of thermal equilibrium to the other. We have already seen that then the number of complexions of the gas increases and consequently also its entropy. The sum of the increments of the number of complexions separately experienced by the two diffusing gases constitutes an increase in the total number of complexions over and above the total number of complexions existing in both gases before diffusion. There is of course a corresponding increase in entropy due to such diffusion.

All these irreversible processes are passages from less stable to more stable conditions, from less probable to more probable states, or summarizing:

There is in Nature a constant tendency to equalize temperature differences, to convert work into heat, to increase disgregation and to promote diffusion.

This tendency has also been described as the tendency in Nature to pass from concentrated to distributed conditions of energy.