As a matter of fact, there was an actual though slight drop in temperature found to exist with the most perfect gases available. Evidently the process was a throttling one, reducing the larger initial pressure to the smaller final one, which reduction was of course accompanied by a corresponding increase in volume.
Assuming that an ideally perfect gas was employed in the experiment, and that the final state for our consideration is that corresponding to its attainment of thermal equilibrium, we see that because of the unchanged temperature there is here no loss of internal energy, for the work consumed by the friction of the porous plug is all returned to the gas by the heat developed by said friction. Moreover, the + and - external work in this experiment also balance. Now although there has been no loss of energy there has been a growth of entropy corresponding to the evident increase in the number of complexions. This increase is exactly equal to that found for reversible isothermal change of state when accompanied by an increase in volume, and the discussion is therefore not repeated here.
One phase of the above process is the conversion of mechanical work into heat through the medium of friction.
INCREASE OF VOLUME WITHOUT PERFORMANCE OF EXTERNAL WORK BY ELASTIC FORCES OF THE GAS
This case of an irreversible process comes into group c. We will consider here JOULE'S well-known experiment with the air tanks, in which the compressed air, initially stored in the one tank, was allowed to discharge into the other tank which, at the start, contained only a vacuum. At the end of the experiment, when thermal equilibrium obtained, the temperature in the two, now connected, tanks was the same as originally existed in the compressed-air tank. Here of course it is assumed that the air exchanged no heat whatever with the outside.
As the final state, like the initial state, is in thermal equilibrium, and possesses the same temperature, we can ascertain the total change in the number of complexions as we did when discussing isothermal and reversible changes and because of the accompanying increase in the volume of the air, find that here as there the number of complexions has increased and that therefore the entropy of the air has increased in this case.
We might rest satisfied with this conclusion, but additional light will be shed on entropy significance if we consider more in detail the intermediate stages of this evidently irreversible process. The rush of air from the full to the empty tank produces whirls and eddies of a finite character and it is only when these have subsided, by the conversion of the visible or sensible kinetic energy of their particles into heat, that thermal equilibrium obtains. But at each intermediate stage (while still visibly whirling and eddying) the gas possesses entropy, even while in the turbulent condition. This is clear from our present physical definition of entropy, namely, the logarithm of the number of complexions of the state, for it is evident that even in this turbulent state it possesses a certain number of complexions, however difficult mathematically it may actually be to find this number. Boltzmann found an expression for any condition; PLANCK gave it the form of Eq. (18), [p. 63],
where
