SECTION DTHE SECOND LAWIt is evident that all these results have for their original basis the Theory of Probabilities. Consequently, because these conclusions are thus based, they must be interpreted according to the general method underlying this Theory. This method essentially is the determination of average (mean) values and calling them the probable ones. We therefore conclude that each state is characterized by the mean number of complexions belonging to that state, that is, by this mean number which changes always in a one-sided way, ever in the same sense, inasmuch as it inevitably and invariably grows till the normal, settled condition is reached.For the sake of clarity we must keep in mind that the motions of the individual atoms are reversible and that in this sense the irreversible processes are reduced to reversible ones. But the process as a whole is not reversible because, by the very act of complete reversal, we would suspend the general, chaotic character of the elementary motions and give them to this extent a special, prearranged feature which would be more or less hostile to the original definition of "elementary chaos." The irreversibility is not in the elementary events themselves, but solely in their irregular arrangement. It is this which guarantees the one-sided change of the mean value characteristic of each one of the successive states of the process.Now remembering that the kernel of the Second Law is that all processes in Nature are irreversible, or, that all changes inNature vary in one direction only, we can, in the light of what of has just preceded, repeat the following precise, scientific statement:"The Second Law, in its objective-physical form (freed from all anthropomorphism) refers to certain mean values which are found from a great number of like and 'chaotic' elements."If we now go back to what constitutes the kernel of the Second Law, we will see the relevance and force of PLANCK'S enunciation of this law:"It is not possible to construct a periodically functioning motor which effects nothing more than the lifting of a load and the cooling of a heat reservoir."The proof of this is purely experimental and cumulative, and the same may be said of the earlier statement of this law, "all changes in Nature vary in one direction only." The character of this proof is, moreover, exactly like that for the First Law, the Conservation of Energy, and has the same sort of validity.When we compared and interpreted the current statements of the Second Law (pp.44-47) we enunciated and made use of three helpful propositions that will now be repeated:(a) All cases of irreversibility stand or fall together; if any one can be reversed all can be reversed.(b) Any general consequence of any one correct statement of the Second Law may be regarded as itself a valid and complete statement of the Second Law.(c) Thesummary of allthe 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 isdirectlyreversible, 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 noindependentsignificance, 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.
It is evident that all these results have for their original basis the Theory of Probabilities. Consequently, because these conclusions are thus based, they must be interpreted according to the general method underlying this Theory. This method essentially is the determination of average (mean) values and calling them the probable ones. We therefore conclude that each state is characterized by the mean number of complexions belonging to that state, that is, by this mean number which changes always in a one-sided way, ever in the same sense, inasmuch as it inevitably and invariably grows till the normal, settled condition is reached.
For the sake of clarity we must keep in mind that the motions of the individual atoms are reversible and that in this sense the irreversible processes are reduced to reversible ones. But the process as a whole is not reversible because, by the very act of complete reversal, we would suspend the general, chaotic character of the elementary motions and give them to this extent a special, prearranged feature which would be more or less hostile to the original definition of "elementary chaos." The irreversibility is not in the elementary events themselves, but solely in their irregular arrangement. It is this which guarantees the one-sided change of the mean value characteristic of each one of the successive states of the process.
Now remembering that the kernel of the Second Law is that all processes in Nature are irreversible, or, that all changes inNature vary in one direction only, we can, in the light of what of has just preceded, repeat the following precise, scientific statement:
"The Second Law, in its objective-physical form (freed from all anthropomorphism) refers to certain mean values which are found from a great number of like and 'chaotic' elements."
If we now go back to what constitutes the kernel of the Second Law, we will see the relevance and force of PLANCK'S enunciation of this law:
"It is not possible to construct a periodically functioning motor which effects nothing more than the lifting of a load and the cooling of a heat reservoir."
The proof of this is purely experimental and cumulative, and the same may be said of the earlier statement of this law, "all changes in Nature vary in one direction only." The character of this proof is, moreover, exactly like that for the First Law, the Conservation of Energy, and has the same sort of validity.
When we compared and interpreted the current statements of the Second Law (pp.44-47) we enunciated and made use of three helpful propositions that will now be repeated:
(a) All cases of irreversibility stand or fall together; if any one can be reversed all can be reversed.
(b) Any general consequence of any one correct statement of the Second Law may be regarded as itself a valid and complete statement of the Second Law.
(c) Thesummary of allthe 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 isdirectlyreversible, 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 noindependentsignificance, 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.