The two laws of thermodynamics (Clausius 1850, Thomson 1851)

1850-1851 Energy and motion theory

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The two laws of thermodynamics: conservation of energy (the first) and the impossibility of the spontaneous passage of heat from a colder body to a warmer one (the second).

The German Rudolf Clausius in Über die bewegende Kraft der Wärme (1850) discarded the conservation of heat, accepted Joule's equivalence of heat and work, and restated Carnot's principle so that its denial would require heat to pass from a colder body to a warmer one. The Briton William Thomson, who in 1849 still wavered between Carnot and Joule, arrived at the same scheme in 1851.

Carnot's principle thus outlived the theory on which it was built.

Why this date

exact

What it grew from

• The analytical theory of heat and Fourier series

  influenced · Confidence: medium

  Fourier was William Thomson's entry into the theory of heat, and it was the notion of conduction, which Thomson had been working on through Fourier in the 1840s, that raised the question of the work lost when heat is merely conducted, the question that led to the dynamical theory of heat.

  Link sources

  • T. N. Narasimhan, Fourier's heat conduction equation: history, influences and connections, Proceedings of the Indian Academy of Sciences (Earth and Planetary Sciences) 108 (3), 117-148 (1999)

    William Thomson (1824-1907), also known as Lord Kelvin, was greatly influenced by Fourier's work. Thomson's first two articles, written at ages 16 and 17, were in defense of Fourier's mathematical approach.

  • Crosbie W. Smith, William Thomson and the Creation of Thermodynamics: 1840-1855, Archive for History of Exact Sciences 16 (3), 231-288 (1977) Verified 20 Sep 2026

    attention was now being focussed on conduction which of course was the very concept with which THOMSON had been dealing during the 1840's in his work on FOURIER.

  "Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.

What grew out of it

• Energetics: physics without atoms

  influenced · Confidence: high

  Ostwald and his allies built energetics on the reliability of thermodynamics: since the two laws work without any hypothesis about the constitution of matter, the atom was declared a superfluous entity.

  Link sources

  • Klodian Coko (rev. of A. Chalmers), Atomism from the 17th to the 20th Century, Stanford Encyclopedia of Philosophy (2026) Verified 20 Sep 2026

    In the late nineteenth century leading scientists such as Ostwald, Duhem and Max Planck were inclined to take thermodynamics as the model of how science should proceed.

  • E. N. Hiebert, H.-G. Körber, Ostwald, Friedrich Wilhelm, Dictionary of Scientific Biography (1978) Verified 20 Sep 2026

    He began seriously to develop his ideas on energetics around 1890, and thereafter gradually reorganized all of his thoughts and work around energy.

  "Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.

Links under review

• "Réflexions sur la puissance motrice du feu" (Carnot)

  influenced · Confidence: high

  The claim rests on a summary in the Wikipedia article. A verbatim quotation is needed from the work it cites: Fox R. (ed.), «Sadi Carnot: Réflexions sur la puissance motrice du feu», critical edition, 1986.

  Carnot's principle (efficiency depending only on temperatures) was retained by Clausius and Thomson after caloric was abandoned and became the second law of thermodynamics.

  Link sources

  • Mendoza E., Britannica (2024) Verified 20 Sep 2026, quotation assembled from fragments

    Though the assumption was incorrect and Carnot himself had doubts about it even while he was writing, many of his results were nevertheless true. ... Eventually Carnot's views were incorporated by the thermodynamic theory as it was developed by Rudolf Clausius in Germany (1850) and William Thomson (later Lord Kelvin) in Britain (1851).

  • Daub E. E., DSB «Clausius» (1971) Verified 20 Sep 2026

    rearranged the traditional argument so that any denial of the premise would require that heat be transferred from a colder to a warmer body, a conclusion which Clausius stated would be an obvious deviation from the normal behavior of heat.

  • de Oliveira, arXiv:2508.17027 (2025) Verified 20 Sep 2026, quotation assembled from fragments

    The Carnot principle was used by Clausius in formulating the second law of thermodynamics ... Clausius rejected part 1 and retained part 2

  • Wikipedia «Reflections on the Motive Power of Fire» (2024) Verified 20 Sep 2026

    Despite the fact that the caloric theory of heat was incorrect, Carnot's work brought together three insights that remain relevant

  "Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong. "Assembled from fragments" means the words do not stand together on the page: we found each fragment separately and joined them with an ellipsis.

• Mechanical equivalent of heat (Joule)

  prerequisite for · Confidence: high

  The claim rests on a summary in the Wikipedia article. A verbatim quotation is needed from the paper itself: Clausius R., «Über die bewegende Kraft der Wärme», Annalen der Physik 79, 1850, or from Fox R., 1971.

  Without Joule's equivalent, Clausius and Thomson could not have replaced the conservation of heat with the conservation of energy.

  Link sources

  • Chemistry World, «Carnot's heat engine and the birth of thermodynamics» (2024)

    By 1850, he and Rudolf Clausius separately reconciled Carnot's ideas about motive power with James Joule's measurements of the equivalence of heat and work, using the concepts of absolute temperature and entropy.

  • Wikipedia «Caloric theory» (2024) Verified 20 Sep 2026

    In 1850, Rudolf Clausius published a paper showing that the two theories were indeed compatible, as long as the calorists' principle of the conservation of heat was replaced by a principle of conservation of energy.

  "Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.

• Kinetic theory of gases and statistical mechanics

  influenced · Confidence: medium

  Both quotations are Boltzmann's own words, and Uffink disputes the first; a historian's judgement on the link between the second law and kinetic theory is still lacking (Brush, The Kind of Motion We Call Heat).

  The second law and Clausius's entropy set the problem that the kinetic theory solved anew, restating the increase of entropy as an increase in the probability of a state.

  Dispute: Both phrases quoted are Boltzmann's own words and not a historian's conclusion, and Uffink rejects the first of them: on his reading the real result is a different one, a generalization of entropy to non-equilibrium states ('The true import of Boltzmann's results is rather that they provide a generalization of the entropy concept to non-equilibrium states'). The influence also runs both ways: Clausius himself built a kinetic theory in 1857 and introduced entropy only in 1865, after Maxwell's 1860 paper.

  Link sources

  • L. Boltzmann (1872), quoted in Jos Uffink, Boltzmann's Work in Statistical Physics, Stanford Encyclopedia of Philosophy (2024) Verified 20 Sep 2026

    This provides an analytical proof of the Second Law in a way completely different from those attempted so far.

  • L. Boltzmann (1877), quoted in Jos Uffink, Boltzmann's Work in Statistical Physics, Stanford Encyclopedia of Philosophy (2024) Verified 20 Sep 2026

    According to the present interpretation, [the Second Law] states nothing else but that the probability of the total state of a composite system always increases

  "Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.

Node sources

• Daub E. E. «Clausius, Rudolf», Dictionary of Scientific Biography (1971) Verified 4 Oct 2026, quotation assembled from fragments

  ...whenever work is produced by heat, a quantity of heat equivalent to that amount of work is consumed—a premise that Clausius believed had been firmly established by Joule’s experiments. The total heat in the universe, therefore, could not be conserved; and the usual concept of heat in a substance, representing the total heat added to that substance, could no longer be considered a function of state.

• Daub E. E. «Clausius, Rudolf», Dictionary of Scientific Biography (1971) Verified 4 Oct 2026, quotation assembled from fragments

  That model for heat perhaps also provided the rationale for his brilliant revision of the traditional Carnot argument in thermodynamics, a revision that made it possible to incorporate the most significant results of the caloric theory within the new theoretical structure. ... Clausius rearranged the traditional argument so that any denial of the premise would require that heat be transferred from a colder to a warmer body, a conclusion which Clausius stated would be an obvious deviation from the normal behavior of heat.

• Daub E. E. «Clausius, Rudolf», Dictionary of Scientific Biography (1971) Verified 4 Oct 2026

  The significant beginning of that career, of course, dates from 1850, when Clausius established the foundations for modern thermodynamics in his first great paper on the theory of heat, “Ueber die bewegende Kraft der Wärme”.

• Daub E. E. «Clausius, Rudolf», Dictionary of Scientific Biography (1971) Verified 4 Oct 2026

  For example, when Kelvin developed his dynamical theory of heat in 1851, he did not explain the function U in terms of molecular energy states.

• Thomson W. «An Account of Carnot's Theory of the Motive Power of Heat», Trans. R. Soc. Edinburgh 16 (1849) Verified 4 Oct 2026, quotation assembled from fragments

  It might appear, that the difficulty would be entirely avoided, by abandoning CARNOT’S fundamental axiom; a view which is strongly urged by Mr JOULE... If we do so, however, we meet with innumerable other difficulties insuperable without farther experimental investigation, and an entire reconstruction of the theory of heat, from its foundation. It is in reality to experiment that we must look either for a verification of CARNOT’S axiom, and an explanation of the difficulty we have been considering; or for an entirely new basis of the Theory of Heat.

"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong. "Assembled from fragments" means the words do not stand together on the page: we found each fragment separately and joined them with an ellipsis.

Further reading

Not evidence: these carry no quotation and support nothing we wrote. They are books and scans to read next.

• Clausius R. «Über die bewegende Kraft der Wärme», Annalen der Physik 79, 368-397, 500-524 (1850)

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