In the history of science, the theory of heat or mechanical theory of heat was a theory, introduced predominantly in 1824 by the French physicist Sadi Carnot, that heat and mechanical work are equivalent. It is related to the mechanical equivalent of heat. Over the next century, with the introduction of the second law of thermodynamics in 1850 by Rudolf Clausius, this theory evolved into the science of thermodynamics. In 1851, in his "On the Dynamical Theory of Heat", William Thomson outlined the view, as based on recent experiments by those such as James Joule, that “heat isn't a substance, but a dynamical form of mechanical effect, we perceive that there must be an equivalence between mechanical work and heat, as between cause and effect.” In the years to follow, the phrase the "dynamical theory of heat" slowly evolved into the new science of thermodynamics. In 1876, for instance, American civil engineer Richard Sears McCulloch, in his Treatise on the Mechanical Theory of Heat, stated that: “the mechanical theory of heat, sometimes called thermo-dynamics, is that branch of science which treats of the phenomena of heat as effects of motion and position.” This term was used in 19th centuries to describe a number of laws, relations, and experimental phenomenon in relation to heat; those such as thermometry, calorimetry, combustion, specific heat, and discussions as to the quantity of heat released or absorbed during the expansion or compression of a gas, etc. One of the most famous publications, in this direction, was the Scottish physicist James Clerk Maxwell’s 1871 book Theory of Heat, which introduced the world to Maxwell's demon, among others. Another famous paper, preceding this one, is the 1850 article On the Motive Power of Heat, and on the Laws which can be deduced from it for the Theory of Heat by the German physicist and mathematician Rudolf Clausius in which the concept of entropy began to take from.
   The term “theory of heat”, being associated with either vibratory motion or energy, was generally used in contrast to the caloric theory, which views heat as a fluid or a weightless gas able to move in and out of pores in solids and found between atoms. In an 1807 journal of Nicholson’s, as an example, we find: “…it is well known that Count Rumford adheres to the old theory of heat being simply a vibratory motion of the particles of bodies.”

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