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Clausius somewhere wrote (in German): ``The energy of the world is constant.'' This is a well known quotation.

What is the source, publication, the rest of the paper?

[Obviously he was summarizing the conservation of energy principle of Mayer by making a trivial inference. Mayer in turn had actually done the water dropping experiment Carnot suggested as a definition and used the mechanical heat equivalent this implied. As far as that energy is conserved but having no idea how energy connects to heat, or proof, that was Leibniz (in his Dynamics). Mayer used the Leibniz terminology. Clausius introduced the word energy later.]

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There is a second sentence to the quote:"The energy of the universe is constant. The entropy of the universe is increasing". The conservation of energy law. The second law of thermodynamics. The quote became famous because from the conjuction of the two conclusion about the heat death of the universe appears to follow. The idea was expressed earlier by Thomson in On the Age of the Sun’s Heat (1862), but Clausius's quip had a nice ring to it.

The quote appears in Ueber Verschiedene für die Anwendung Bequeme Formen der Hauptgleichungen der Mechanischen Wärmetheorie (On Several Applications of the Main Equations of the Mechanical Theory of Heat), Annalen der Physik und Chemie., vol. 125 No. 7 (1865): pp. 353–400. Here is a direct link to the paper.

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    $\begingroup$ The quote is the paper's very last sentence, p. 400. $\endgroup$ – Francois Ziegler Oct 28 '15 at 14:49
  • $\begingroup$ As an aside, it is now known that the total energy of the universe is not constant, since the FLRW metric is time-dependent. $\endgroup$ – Danu Oct 29 '15 at 14:15
  • $\begingroup$ @Danu: It's correct that the total energy of the universe is not constant, but this does not follow from the fact that the metric is time-varying. For example, the energy of an asymptotically flat spacetime is conserved, regardless of whether the metric is time-varying. $\endgroup$ – Ben Crowell Oct 29 '15 at 14:27
  • $\begingroup$ @BenCrowell You're correct---I was being sloppy. $\endgroup$ – Danu Oct 29 '15 at 14:45

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