If we consider only heat and mechanical phenomena and do not include electrical occurrences, the irreversible processes may be grouped in four classes:
(a) The body whose changes of state are considered is in contact with one or more bodies whose temperatures differ by a finite amount from its own. There is here flow of heat from hot to cold and the process is an irreversible one.
(b) When the body experiences friction which develops heat it is not possible to effect completely the opposite operation.
(c) The third group includes those changes of state in which a body expands without at the same time developing an amount of external energy which is exactly equal to the work of its elastic forces. For example this occurs when the pressure which a body has to overcome is essentially (that is, finitely) less than the body's own internal tension. In such a case it is not possible to bring said body back to its initial state by a completely opposite procedure. Examples of this group are: steam escaping from a high-pressure boiler, compressed air flowing into a vacuum tank and a spring suddenly released from its state of high tension.
(d) Suppose two gases existing at the same pressure and temperature are on opposite sides of a partition; when the partition is quickly removed the two gases will diffuse or mix. These gases will not unmix of themselves and the diffusion process is an irreversible one and is somewhat like the process considered under (c).
The foregoing facts and propositions have in the main already been stated in this presentation and it will be profitable to make comparisons with the definition of irreversible and reversible events given on [p. 30] and with the examples on pp. [31], [32].
HEAT CONDUCTION
The group under head (a) represents the irreversible processes which perhaps occur most often, namely, the direct passage of heat, by conduction or radiation, from a hot body to a cold body, here say from a hot gas to a cold gas. The former loses in heat energy what the latter gains. As radiation phenomena have very special features of their own and for the present may be said to be outside of our selected province, we will confine our attention to heat conduction alone. Moreover, for our present purpose, we will suppose said flow or change to take place without alteration of volume of either the hot or the cold gas. Then will the hot gas experience a drop in temperature and the cold one a rise in temperature. We have already treated such isometric changes and know that the number of complexions is thereby diminished in the originally hotter body and increased in the originally colder one. If this increment is greater than the accompanying decrement, then the final outcome of this direct passage from hot to cold is an increase in the total number of complexions of the two gases. There will then, by our precise definition, be a corresponding increase in the total entropy of the two systems. It is foreign to our present purpose to prove in an independent, purely mechanical way, that such excess does finally exist and will here content ourselves with the well-known and simple thermodynamic expression for this excess,
where