The Thermodynamic Origins of Entropy: Carnot and The Heat Engine

Carnot, Caloric Theory and The Heat Engine

In 1823 when Sadi Carnot (1796–1832) began this task, less than thirty years had passed since Rumford’s cannon-boring experiments led him to declare “heat is motion”. And although this should have been the end of caloric theory, it and its principle of heat (caloric) conservation were mostly undaunted. Further, a more complete understanding of energy would have to wait for some thirty years for the first law to be established.

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The Universal Tendency of Energy

William Thomson’s Struggle with Heat and Work

In 1847, when William Thomson (later Lord Kelvin) (1824–1907) learned of Joule’s experiments (on the mechanical equivalent of heat) demonstrating that work could be converted to heat, he immediately recognized the impact of this discovery. Moreover, it was clear, although not explicitly demonstrated by Joule’s experiments (but nonetheless claimed by Joule), that this equivalence meant that one would expect the conversion of heat into work to be possible as well. This caused problems for Thomson, since at that time, he was still a proponent of caloric theory, which stood in direct opposition to Joule’s conclusion.

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Carnot the Outsider

During his formal education Sadi Carnot (1796-1832) was literally surrounded by renowned physicist, chemists and mathematicians on the faculty. However, Carnot was never a member of this distinguished group, and did his most important work (as a founder of modern day thermodynamics) as an outsider.

The Drinking Bird as a Heat Engine

The drinking bird is a nice example of a heat engine. The evaporation of water at the bird’s beak results in a cooler temperature there than at its base (around the tail feather). In turn, this temperature difference causes a pressure difference (high to low from base to beak) that causes the (very volatile) liquid to rise up, eventually toppling the bird forward causing it to “drink”.

The Drinking Bird

Heat as “Caloric”

Pierre-Simon Laplace (1749-1827) imagined heat to be a fluid composed of particles, deemed by Antoine Lavoisier (1743-1794) as “caloric”.

Clapeyron’s Reformulation of Carnot’s Work

In 1834 Émile Clapeyron (1799-1864), a former classmate of Carnot’s, published a paper in the Journal de l’École Polytechnique. Here he reformulated Carnot’s work using clear concise mathematics and a new graphical presentation for Carnot’s reversible heat engine (still taught today to every chemistry major taking a good physical chemistry class) that finally brought Carnot’s work to the attention of engineers, chemists and physicists.

Energy and Entropy

Energy and the first law that governs it can’t explain why certain processes tend in what apparently is a favored direction; for that we need entropy.

Energy, Entropy and the Universe

Whereas the universe keeps energy at a constant (energy is conserved), it continues to increase the entropy. Therefore, no process that occurs will ever result in an overall decrease in the entropy of the universe. The universes’ tendency of maximizing entropy is reminiscent of “a universal tendency to the dissipation of mechanical energy” as stated by Thomson, and Clausius noted the connection.

Heat is Energy

Heat was the biggest stumbling block to a complete understanding of energy, remaining separate from it until around 1850 when the first law of thermodynamics was inducted.

Confusion About Energy

An understanding of energy in its entirety did not occur until well into the nineteenth century.