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Updated: June 6, 2025


Starting with this principle, we arrive, as does Clausius, at the demonstration that the output of a reversible machine working between two given temperatures is greater than that of any non-reversible engine, and that it is the same for all reversible machines working between these two temperatures.

It is to Clausius that was reserved the credit of rediscovering the principle, and of enunciating it in language conformable to the new doctrines, while giving it a much greater generality.

Clausius' and Maxwell's explanations of the diffusion of gases, and of thermal conduction in gases, their charmingly intelligible conclusion that in gases the diffusion of heat is just a little more rapid than the diffusion of molecules, because of the interchange of energy in collisions between molecules, while the chief transference of heat is by actual transport of the molecules themselves, and Maxwell's explanation of the viscosity of gases, with the absolute numerical relations which the work of those two great discoverers found among the three properties of diffusion, thermal conduction, and viscosity, have annexed to the domain of science a vast and ever growing province.

This is the very proposition of Carnot; but the proposition thus stated, while very useful for the theory of engines, does not yet present any very general interest. Clausius, however, drew from it much more important consequences.

M. Clausius has determined the mean length of path in terms of the average of the particles, and the distance between the centres of two particles when the collision takes place.

Clausius put it in a negative form, as thus: No engine can of itself, without the aid of external agency, transfer heat from a body at low temperature to a body at a high temperature. Cf. Ganot's Physics, 17th English edition, § 508. In the minds of many persons, however, grave doubts persisted. Solution appeared to be an essentially irreversible phenomenon.

Siemens had been trained as a mechanical engineer, and, although he became an eminent electrician in later life, his most important work at this early stage was non-electrical; indeed, the greatest achievement of his life was non-electrical, for we must regard the regenerative furnace as his MAGNUM OPUS. Though in 1847 he published a paper in Liebig's ANNALEN DER CHEMIE on the 'Mercaptan of Selenium, his mind was busy with the new ideas upon the nature of heat which were promulgated by Carnot, Clayperon, Joule, Clausius, Mayer, Thomson, and Rankine.

Clausius and Lord Kelvin have drawn from these considerations certain well-known consequences on the evolution of the Universe.

Daniel Bournelli, Herapath, Joule, Kronig, Clausius, etc., have shown that the relations between pressure, temperature, and density in a perfect gas can be explained by supposing the particles to move with uniform velocities in straight lines, striking against the sides of the containing vessel and thus producing pressure.

Clausius was the first to point out how this might be done from a knowledge of the length of free path; and the calculations were made by Loschmidt in Germany and by Lord Kelvin in England, independently. The work is purely mathematical, of course, but the results are regarded as unassailable; indeed, Lord Kelvin speaks of them as being absolutely demonstrative within certain limits of accuracy.

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