The expected increase of fuel efficiency of the engine ( caused by the higher temperature, as shown by Carnot's theorem ) could not be verified experimentally ; it was found that the heat transfer on the hot ceramic cylinder walls is higher than the transfer to a cooler metal wall.

Heat engines distinguish themselves from other types of engines by the fact that their efficiency is fundamentally limited by Carnot's theorem .< ref > Thermal physics: entropy and free energies, by Joon Chang Lee ( 2002 ), Appendix A, p. 183: " A heat engine absorbs energy from a heat source and then converts it into work for us.

Carnot's theorem ( 1824 ) is a principle that limits the maximum efficiency for any possible engine.

Carnot's theorem states:

Carnot's theorem states that all reversible engines operating between the same heat reservoirs are equally efficient.

* Carnot's theorem in geometry.

Carnot's theorem reveals the absolute limit of efficiency:

Carnot's theorem states:

Based on modern thermodynamics, Carnot's theorem is a result of the second law of thermodynamics.

In Euclidean geometry, Carnot's theorem, named after Lazare Carnot ( 1753 – 1823 ), is as follows.

Carnot's theorem is used in a proof of the Japanese theorem for concyclic polygons.

In most heat engines, a bit more than half is lost as excess heat ( see: Second law of thermodynamics and Carnot's theorem ).

# redirect Carnot's theorem

Due to Carnot's theorem, a heat engine cannot be 100 % efficient ; it cannot convert anywhere near all the heat in the fuel it burns into useful forms such as electricity.

In 1843, Clapeyron further developed the idea of a reversible process, already suggested by Carnot and made a definitive statement of Carnot's principle, what is now known as the second law of thermodynamics.

In the adjacent diagram, from Carnot's 1824 work, Reflections on the Motive Power of Fire, there are " two bodies A and B, kept each at a constant temperature, that of A being higher than that of B.

Lavoisier's prestige and the practical success of Sadi Carnot's caloric theory of the heat engine since 1824 ensured that the young Joule, working outside either academia or the engineering profession, had a difficult road ahead.

* Carnot's rule, an early formulation of the second law of thermodynamics.

The advantage of gasification is that using the syngas is potentially more efficient than direct combustion of the original fuel because it can be combusted at higher temperatures or even in fuel cells, so that the thermodynamic upper limit to the efficiency defined by Carnot's rule is higher or not applicable.

According to Carnot's principle, work can only be done when there is a temperature difference, and the work should be some function of the difference in temperature and the heat absorbed.

If a real-world reference environment is chosen that behaves like an unlimited reservoir that remains unaltered by the system, then Carnot's speculation about the consequences of a system heading towards equilibrium with time is addressed by two equivalent mathematical statements.

It has, as we know, as a measure, the product of the weight multiplied by the height to which it is raised .” With the inclusion of a unit of time in Carnot's definition, one arrives at the modern definition for power:

Then Clausius asked what would happen if there would be less work done than that predicted by Carnot's principle.

* 1850 – Rudolf Clausius gives the first clear joint statement of the first and second law of thermodynamics, abandoning the caloric theory, but preserving Carnot's principle.

By his restatement of Sadi Carnot's principle known as the Carnot cycle, he put the theory of heat on a truer and sounder basis.

In this paper, he showed that there was a contradiction between Carnot's principle and the concept of conservation of energy.

::-Rudolf Clausius gives the first clear joint statement of the first and second law of thermodynamics, abandoning the caloric theory, but preserving Carnot's principle.

Carnot's principle and reformation theory.

President Carnot's ostensible part during this agitation was confined to augmenting his popularity by well-timed appearances on public occasions, which gained credit for the presidency and the republic.

" The Oxford English Dictionary cites the first English-language usage in 1799 in a translation of Lazare Carnot's letter on the Coup of 18 Fructidor.

Clapeyron, in his memoire, presented Carnot's work in a more accessible and analytic graphical form, showing the Carnot cycle as a closed curve on an indicator diagram, a chart of pressure against volume ( named in his honor Clapeyron's graph ).

In any case, only Carnot's account reached Paris.

Axis of rotation | Axial Cross section ( geometry ) | cross section of Carnot's heat engine.

Kelvin suggested that the best temperature scale would describe a constant ability for a unit of temperature in the surroundings to alter the available work from Carnot's engine.

This relation transforms the Carnot's inequality into exact equality.

By 1858, thermo-dynamics, as a functional term, was used in William Thomson's paper An Account of Carnot's Theory of the Motive Power of Heat.

* 1834 – Émile Clapeyron popularises Carnot's work through a graphical and analytic formulation.

Though Thomson conducted no new experiments, over the next two years he became increasingly dissatisfied with Carnot's theory and convinced of Joule's.

Depiction of Carnot's assassination appearing in Le Petit Journal | Le Petit Journal Illustré. When the Daniel Wilson scandals occasioned the downfall of Jules Grévy in December 1887, Carnot's reputation for integrity made him a candidate for the presidency, and he obtained the support of Georges Clemenceau and many others, so that he was elected by 616 votes out of 827.

Carnot's talents as ' the organizer of victory ' are beyond dispute, but his tactical skills were minimal, a defect he concealed by a careful rewriting of history.

Namely, such a null sequence becomes an infinitesimal in Cauchy's and Lazare Carnot's terminology.