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Rumford's experiment inspired the work of James Prescott Joule and others towards the middle of the 19th century. 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. Although compatible however, the theories differ significantly in their implications. In modern thermodynamics, heat is usually a transfer of kinetic energy of particles (atoms, molecules) from a hotter to a colder substance. In later combination with the law of energy conservation, the caloric theory still provides a valuable analogy for some aspects of heat, for example, the emergence of Laplace's equation and Poisson's equation in the problems of spatial distribution of heat and temperature.

== See also == Energeticisms

== Notes ==

== References ==

=== Citations ===

=== Sources cited === Best, Nicholas W. (2015). "Lavoisier's "Reflections on phlogiston" II: on the nature of heat". Foundations of Chemistry. 18 (1): 313. doi:10.1007/s10698-015-9236-x. ISSN 1386-4238. Page numbers in square brackets are from Lavoisier, A.-L. (186293) [1786]. Réflexions sur le phlogistique, pour servir de suite à la théorie de la combustion et de la calcination, publiée en 1777. In Dumas, J.-B.; Grimaux, E.; Fouqué, F.-A. (eds.). Œuvres de Lavoisier, Vol. II. Imprimerie Impériale. pp. 623655. The subtitle On the Nature of Heat is not part of Lavoisiers original work.{{cite journal}}: CS1 maint: postscript (link) Fox, R. (1971). The Caloric Theory of Gases. Clarendon Press: Oxford. Chang, H.S. (2003). "Preservative realism and its discontents: Revisiting caloric" (PDF). Philosophy of Science. 70 (5): 902912. doi:10.1086/377376. S2CID 40143106. Mendosa, E. (February 1961). "A sketch for a history of early thermodynamics". Physics Today. 14 (2): 3242. Bibcode:1961PhT....14b..32M. doi:10.1063/1.3057388.