SECTION FMORE PRECISE AND SPECIFIC STATEMENTS OF THE SECOND LAWWe have here classified these statements in the same way as that followed in the preceding section, when grouping thegeneralequivalents of theSecond Lawunder the head ofchange of entropy. In making comparisons we must, here as there, bear in mind the following three helpful propositions:(a) The summary ofallthe necessary prerequisites (or conditions) for determining entropy may be regarded as a complete and valid statement of the second law.(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) All cases of irreversibility stand or fall together; if any one of them can be completely reversed all can be so reversed.In the preceding section we have already given the most precise physical statement of the Second Law, namely, when all the participating bodies of the system are considered, every natural event is marked by an increase in the number of complexions of the system. We have numbered the following statements of the second law, for convenience of reference:(1) J. W. GIBBS. "The impossibility of an uncompensated decrease in entropy seems to be reduced to an improbability." This of course considersallthe participating bodies of the system.(2) All changes in nature involve a net growth in entropy; when such a change is measured in reversible ways, the growth is indicated by the summation:, when thesign refers to processes which on the whole are completely. Of course it is now thoroughly understood that the latter case is a purelyideal one, which is really never realized in nature and is only a convenient and fruitful fiction in theoretical demonstrations.(3) M. PLANCK. "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 in this respect is exactly like that for the First Law, the Conservation of Energy, and has exactly the same sort of validity.(4) Perpetual motion of an isolated system, such as a mechanism with friction, is impossible and not even approximately realizable.This refers to perpetual motion of the second class, a clear illustration of which is given on p. 8 of Goodenough's Notes on Thermodynamics: "A mechanism with friction is inclosed in a case through which no energy passes. Let the mechanism be started in motion. Because of friction work is converted into heat which remains in the system, since no energy passes through the case. Suppose that the heat thus produced could be completely transformed into work; then this work would be used again to overcome friction and the heat thus produced would be again transformed into work. We should then have perpetual motion in a mechanism with friction without the addition of energy from an external source." This can be shown to be equivalent but not identical with the "perpetual motion of the second kind," touched upon inp. 30; the latter does confessedly draw on external energy and furnishes a surplus of power for use, say, in technical service.Nominally, such a machine is a case of perpetual motion, but not in the usually accepted sense, for it furnishes nosurplusof power; it is the getting of something for nothing, of getting cost-free power, which has always been the attractive feature of so-called perpetual motion. Still this machine is as much at variance with experience as PLANCK'S perpetually working motor of thesecond kind. The former may be readily reduced to the latter, for it is easy to conceive of such legitimate modification of the former as will make it only a special case of the latter.(5) The following statements are by distinguished physicists and had better here be considered as confined to events occurring in closed cycles.CLAUSIUS. It is impossible for a self-acting machine unaided by any external agency to convey heat from one body to another of higher temperature.CLERK MAXWELL. It is impossible by the unaided action of natural processes to transform any part of the heat of a body into mechanical work, except by allowing heat to pass from that body to another of lower temperature.THOMSON. It is impossible by means of inanimate material agency to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of surrounding objects.(6) The efficiency of a perfect engine is independent of the working fluid.(7) Waste of energy once incurred cannot be diminished in the universe, or in any part of it which neither takes in nor gives out energy.We understand here by waste that residual part of heat of which none can be elevated back into work.The measure of such waste =, when= lowest temperature and= change of entropy in a process. This brings out emphatically that the Second Law is not a law of conservation, it is a law of waste, a law of wasted opportunities for utilizing technically available energy.(8) The second law and irreversibility do not depend on any special peculiarity of heat motion, but only on the statistical property of a system possessing an extraordinary number of degrees of freedom.(9) M. PLANCK. The second law, in its objective physicalform (freed from all anthropomorphism) refers to certainmeanvalues which are formed from a great number of like "chaotic" elements.(10) When all the participating bodies of the system are considered, every natural event is marked by an increase in the number of complexions of the system. We repeat, this is the most precise physical statement of the second law and covers the whole domain of science.We will not comment further on these statements at this time, leaving such discussion of their relations to the section on physical interpretations.
MORE PRECISE AND SPECIFIC STATEMENTS OF THE SECOND LAW
We have here classified these statements in the same way as that followed in the preceding section, when grouping thegeneralequivalents of theSecond Lawunder the head ofchange of entropy. In making comparisons we must, here as there, bear in mind the following three helpful propositions:
(a) The summary ofallthe necessary prerequisites (or conditions) for determining entropy may be regarded as a complete and valid statement of the second law.
(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) All cases of irreversibility stand or fall together; if any one of them can be completely reversed all can be so reversed.
In the preceding section we have already given the most precise physical statement of the Second Law, namely, when all the participating bodies of the system are considered, every natural event is marked by an increase in the number of complexions of the system. We have numbered the following statements of the second law, for convenience of reference:
(1) J. W. GIBBS. "The impossibility of an uncompensated decrease in entropy seems to be reduced to an improbability." This of course considersallthe participating bodies of the system.
(2) All changes in nature involve a net growth in entropy; when such a change is measured in reversible ways, the growth is indicated by the summation:, when thesign refers to processes which on the whole are completely. Of course it is now thoroughly understood that the latter case is a purelyideal one, which is really never realized in nature and is only a convenient and fruitful fiction in theoretical demonstrations.
(3) M. PLANCK. "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 in this respect is exactly like that for the First Law, the Conservation of Energy, and has exactly the same sort of validity.
(4) Perpetual motion of an isolated system, such as a mechanism with friction, is impossible and not even approximately realizable.
This refers to perpetual motion of the second class, a clear illustration of which is given on p. 8 of Goodenough's Notes on Thermodynamics: "A mechanism with friction is inclosed in a case through which no energy passes. Let the mechanism be started in motion. Because of friction work is converted into heat which remains in the system, since no energy passes through the case. Suppose that the heat thus produced could be completely transformed into work; then this work would be used again to overcome friction and the heat thus produced would be again transformed into work. We should then have perpetual motion in a mechanism with friction without the addition of energy from an external source." This can be shown to be equivalent but not identical with the "perpetual motion of the second kind," touched upon inp. 30; the latter does confessedly draw on external energy and furnishes a surplus of power for use, say, in technical service.
Nominally, such a machine is a case of perpetual motion, but not in the usually accepted sense, for it furnishes nosurplusof power; it is the getting of something for nothing, of getting cost-free power, which has always been the attractive feature of so-called perpetual motion. Still this machine is as much at variance with experience as PLANCK'S perpetually working motor of thesecond kind. The former may be readily reduced to the latter, for it is easy to conceive of such legitimate modification of the former as will make it only a special case of the latter.
(5) The following statements are by distinguished physicists and had better here be considered as confined to events occurring in closed cycles.
CLAUSIUS. It is impossible for a self-acting machine unaided by any external agency to convey heat from one body to another of higher temperature.
CLERK MAXWELL. It is impossible by the unaided action of natural processes to transform any part of the heat of a body into mechanical work, except by allowing heat to pass from that body to another of lower temperature.
THOMSON. It is impossible by means of inanimate material agency to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of surrounding objects.
(6) The efficiency of a perfect engine is independent of the working fluid.
(7) Waste of energy once incurred cannot be diminished in the universe, or in any part of it which neither takes in nor gives out energy.
We understand here by waste that residual part of heat of which none can be elevated back into work.
The measure of such waste =, when= lowest temperature and= change of entropy in a process. This brings out emphatically that the Second Law is not a law of conservation, it is a law of waste, a law of wasted opportunities for utilizing technically available energy.
(8) The second law and irreversibility do not depend on any special peculiarity of heat motion, but only on the statistical property of a system possessing an extraordinary number of degrees of freedom.
(9) M. PLANCK. The second law, in its objective physicalform (freed from all anthropomorphism) refers to certainmeanvalues which are formed from a great number of like "chaotic" elements.
(10) When all the participating bodies of the system are considered, every natural event is marked by an increase in the number of complexions of the system. We repeat, this is the most precise physical statement of the second law and covers the whole domain of science.
We will not comment further on these statements at this time, leaving such discussion of their relations to the section on physical interpretations.