(c) The summary of all the necessary prerequisites (or conditions) for determining Entropy may be regarded as a complete and valid statement of the Second Law.
In this connection it will also be helpful to remember PLANCK'S statement: "In order that a process may be truly reversible it will not suffice to declare that the mediating body is directly reversible, but that at the end, everywhere in the whole of Nature, the same state must be restored which existed at the beginning of said reversible process."
As regards the use of helpful proposition (a):
We know that PLANCK'S motor statement of the Second Law was grounded on the well-known irreversible passage of heat from a cold to a hot body. But to show the mutual interdependence (a) of one irreversible change on every other, we will instance in illustration the case of a frictional event, or the conversion of mechanical work into heat.
If this frictional occurrence could by any simple or complex apparatus be made completely reversible so that everywhere, in the whole of Nature, the same state would be restored which existed at the beginning of the frictional occurrence, then such an apparatus would be the motor contemplated in PLANCK'S statement of the Second Law, for this periodically running apparatus would convert heat into work without any other change remaining. A similar line of argument, with a similar result, could be pursued with every other case of irreversibility that could be adduced. It is evident that, with the help of the above-given propositions (a), (b), and (c), the Second Law can be cast into many other valid forms.
We close this presentation of the meaning of the Second Law by the remark that this law has no independent significance, for its roots go down deep into the Theory of Probabilities. It is therefore conceivable that it is applicable to some purely human and animate events as well as to inanimate, natural events; provided, of course, that the former possess numerous like and uncontrolled constituents which may be properly characterized as "elementar-ungeordnet," in other words, provided the variable elements present constitute adequate haphazard for the Calculus of Probabilities.
PART V
REACH AND SCOPE OF SECOND LAW
SECTION A
ITS EXTENSION TO ALL BODIES
CLAUSIUS extended the operation of the Second Law or, what is the same thing, the scope of entropy, to all bodies. See RÜHLMANN'S "Handbuch d. mech. Wärmtheorie," Vol. I, pp. 395-405.
BOLTZMANN says in this connection: "As regards entropy, solid and liquid bodies do not differ qualitatively from perfect gases; the discussion of the entropy of the former, however, presents greater mathematical difficulties."