Clausius' Theory of Heat *** ***

"If Clausius and Kelvin were "fathers of thermodynamics" then Sadi Carnot was the "grandfather" or better yet,
Sadi Carnot was the "FOREFATHER of Thermodynamics-to-become" [M Kostic, 2023 October 29]

See 2LT * Selected Presentations at Speaking, Lecturing, and Media
Also,  Proofs of the Fundamental Laws *  Carnot Cycle Efficiency is Fundamentally Misplaced *

See also: > Sadi Carnot's Reflections <*> Clausius Theory of Heat <*> Kelvin Theory of Heat <

Clausius, R. The Mechanical Theory of Heat (English translation by W.R. Browne), McMillan and Co., London 1879.

Click (or Right-Click) on the above title-link or here to download the publication 

(23912 KB, 390 pages large PDF file) Hosted by Prof. M. Kostic at 

More at:
Also:  Rudolf Clausius (1822 - 1888) - Biography - MacTutor History of Mathematics ( 

See also "On the Dynamical Theory of Heat" by Lord Kelvin (William Thomson)

Note, Joule's "the mechanical equivalent of heat" versus Carnot's "motive power of heat."

"Entropy is associated with stored-heat within a material system, i.e. its thermal energy. It is an integral measure of thermal energy per absolute temperature of a system. As heat is generated due to dissipation of any work potential to heat, the entropy is produced. However, if heat is converted to work (like in heat engines), the thermal energy is reduced while transferred to a lower-temperature thermal reservoir, however, the entropy (as ratio of thermal heat to absolute temperature) will not be reduced but conserved in ideal, reversible processes (Qrev/T=const, Carnot Ratio Equality), or even the entropy will be produced (generated) in real (irreversible) processes for the amount of dissipated work-potential to stored heat (or thermal energy) per absolute temperature, regardless that the thermal energy is reduced (converted to work). Therefore, the entropy is always produced, locally and thus integrally or globally, and there is no way to destroy entropy, since it will be against the forced energy transfer from higher to lower potential  [Kostic: 2008 & 2011 & 2014 & 2020 & 2023]. ."

"Reflections on the Caloric Theory and Thermal Energy as a Distinguished Part of the Internal Energy

Nature of heat was a mystery for a long time. Lavoisier proposed that "heat is a subtle, weightless substance called caloric." Being a substance, the conservation of caloric was a central assumption, long before the energy conservation was established. Furthermore, the kinetic theory existed in the late eighteenth century that could explain the heat and other thermal phenomena. Regardless of ingenious developments, the Caloric Theory has been discredited since the caloric was not obviously conserved during heat generation processes, like drilling, and similar. In modern times, there is a tendency by some scientists to unduly discredit "thermal energy"as being indistinguishable from other internal energy types. Denying the existence of thermal energy is the same as denying the existence of its transfer (heat transfer). Some others consider the Thermodynamic internal energy to be the thermal energy, although the former represents all energy types stored as the kinetic and potential energies of the constituent microstructure, namely, the thermal and mechanical elastic energies in simple compressible substances, in addition to the chemical and nuclear internal energies. In a more complex system-structure there may be more energy types. The stored system heat increases the system's thermal energy which is distinguished from the system's internal, mechanical (elastic) energy. For example, the heating or compressing an ideal gas with the same amount of energy will result in the same temperatures and internal energies, but different states, with different volumes and entropies, and similar for other material substances. Reversible heat transfer and caloric heat transfer, without work interactions, are introduced as limiting processes of heat-work interactions. It is reasoned and deduced here [Reflections], that the thermal energy is distinguishable, regardless of its coupling with the other internal energy forms, and thus paves the way to further illuminate other critical concepts, including Thermodynamic entropy and the Second Law of energy degradation and entropy generation.

mechanical equivalent of heat

"Nothing occurs locally, nor globally in the universe, without mass-energy exchange/conversion and entropy production. 

It is crystal-clear (to me) that all confusions related to the far-reaching fundamental Laws of Thermodynamics, and especially the Second Law (Abstract & FULL paper), are due to the lack of their genuine and subtle comprehension." > Sadi Carnot's Reflections <*> Clausius Theory of Heat <*> Kelvin Theory of Heat <