# Nature of Heat and Thermal Energy: From Caloric to Carnot’s Reflections, to Entropy, Exergy, Entransy and Beyond

## Abstract

**:**

## 1. Introduction—From Caloric to Carnot’s Reflections

## 2. Nature of Thermo—Mechanical Energy Transfer

^{2}) through material systems involved, from a mass-energy source to a sink system, as depicted on Figure 1, and detailed in its caption. Ironically, Lavoisier was correct that caloric is a substance, but not weightless. More details were presented [8] and will be published after updates are finalized.

## 3. Nature of Heat and Thermal Energy

## 4. Entropy: Thermal (Chaotic-Dynamic) Displacement

## 5. Maxwell’s Demon and Second Law Challenges

## 6. Exergy and Entransy, and Beyond

_{B}< T

_{A}). The mutual work-potential (W

_{Rev}) is fully dissipated with related entropy generation (S

_{AB,Gen}) during the irreversible process leading to mutual equilibrium at T

_{AB}= T

_{AB,Irr}.

_{AB,Rev}with entropy changes, but without entropy generation:

_{AB,Rev}(Equation (2)), smaller than in spontaneous irreversible case at T

_{AB}= T

_{AB,Irr}, since the work potential will dissipate within the combined system instead of being extracted out, i.e.,:

_{Rev}and entropy generation S

_{AB,Gen}are not related, and thus not dependent on any reference, surrounding dead-state (P

_{o}, T

_{o}), since the combined system (A + B) is isolated from its surrounding. However, it is capable of producing (extracting) work due to its initial non-equilibrium. That work-potential is completely dissipated (heat generation within) after coming spontaneously (irreversibly) in mutual equilibrium. Actually, the required condition for spontaneous process is the existence of “mutual, non-equilibrium work potential”. The “exergy” is “hypothetical work-potential” if a system reversibly comes to equilibrium by interacting with an arbitrary reference dead-state system (i.e., surrounding). Exergy is useful for comparison, and practical if our systems are coming in equilibrium with such a reference surrounding (i.e., the case with many engineering processes and the Earth’s surroundings, i.e., environment).

_{Bry}) at finite temperature difference may be considered as reversible at boundary temperature T

_{Bry}, and that the irreversibility takes place within the system when the boundary heat is received at a lower system temperature T

_{Sys}, thus resulting in generated heat and the remaining reversible heat at the system level (heat totality, such as original caloric, conserved). This may be perplexing, since it depends where the irreversibility takes place (whether the temperature gradients are within a layer close to the boundary on the system or surrounding’s sides, or within the system), but if properly accounted for, it will result in the same outcome.

_{B}to T

_{AB}, instead with system A, but with another system B

^{+}with variable temperature, always infinitesimally higher than A’s, then such a process would be reversible (in limit) and without (or infinitesimally small) entropy generation. The entropy (a system property) is subtle and so is irreversible entropy generation (a process quantity), that it becomes the property after the process is finished.

_{Loss}= W

_{Diss}= Q

_{Gen}) and entropy generation (S

_{Gen}) are function of the initial and final process states’ properties only, and not of any other reference dead-state, as it might allude at first, since the combined system (A + B) is isolated from the surrounding, i.e., it comes to mutual equilibrium, and does not interact with the surrounding.

_{o}& P

_{o}, the exergy of heat Q

_{1}from a reservoir at temperature T

_{1}is E

_{x}

_{1}= Q

_{1}(1 − T

_{o}/T

_{1}) and at state 2 would be E

_{x}

_{2}= Q

_{2}(1 − T

_{o}/T

_{2}). It appears that the exergy difference, E

_{x}

_{1}− E

_{x}

_{2}, is a function of T

_{o}. However, for reversible cycle, Q

_{2}/T

_{2}= Q

_{1}/T

_{1}(Carnot ratio equality), the relevant quantities are correlated, so the above is reduced to:

_{x1}− E

_{x2}= Q

_{1}(1 − T

_{o}/T

_{1}) − Q

_{2}(1 − T

_{o}/T

_{2}) = Q

_{1}(1 − T

_{o}/T

_{1}) − (Q

_{1}·T

_{2}/T

_{1})(1 − T

_{o}/T

_{2}) = (Q

_{1}/T

_{1})(T

_{1}− T

_{2})

_{o}. Therefore, it is unnecessary to use exergy (which is based on a hypothetical reference, surrounding dead-state, T

_{o}, P

_{o}). Furthermore, for isolated processes without interaction with the surrounding, it may be inappropriate, to use exergy difference, since actual work-loss is relative to mutual equilibrium state reached between the two isolated sub/systems, as demonstrated above (there is no T

_{o}and P

_{o}in the above expressions). It may be the case for all thermal processes with no net-entropic, nor net-volumetric interactions with the surrounding. It requires further discussions and clarifications.

_{ve}= I·t = E

_{e}/V), and heat conduction, is introduced from Q

_{vh}= Z

_{tr}/T = E

_{vh}/T = G/T (as concept-in-general, if electrical charge and heat are transferred at constant voltage and temperature, respectively), thus, in principle, defining a new physical quantity, “entransy” [15,16,17,18], i.e.,:

_{vh}), has been utilized for stored heat as thermal energy within the material system, For the new quantity, entransy different symbols have been used in subsequent publications.

_{v}= f(P, T) ≈ f(T), i.e.,

_{v}TdT

_{REV}, entransy dissipation or loss G

_{LOSS}, and Carnot work-potential loss W

_{LOSS}is presented on Figure 8.

_{W}, is also essential to be defined for processes when thermal heat is converted to work, such as in heat engines. The work entransy could be defined using the entransy balance for reversible, Carnot cycle relationship, and considering that there is no entransy loss in an ideal reversible process, i.e., G

_{IN}= G

_{OUT}or G

_{1}= G

_{W}+ G

_{2}(notation in [18]):

_{W}= G

_{1}− G

_{2}= G

_{1}(1 − (T

_{2}

^{2}/T

_{1}

^{2})) or dG

_{W}= (1 − (T

_{2}

^{2}/T

_{1}

^{2}))·dG

_{1}

_{W}, was derived by algebraic manipulation as G

_{W}= WT

_{1}= (Q

_{1}− Q

_{2})T

_{1}= Q

_{1}(T

_{1}− T

_{2}). However, this definition is not appropriate since it does not satisfy condition that entransy loss is zero for reversible processes. There is a need for further interpretations of the entransy concept and possible refinements [18].

## 7. Challenges and Concluding Remarks

_{Th}≡ Q

_{Stored}, and heat is the thermal energy transfer, Q ≡ U

_{Th,transfer}, [10].

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Electromagnetic nature of thermo-mechanical mass-energy transfer due to photon diffusive re-emission and propagation. Based on atomic electron-shell interactions and the Einstein mass-energy equivalence, during “believed-massless” heat conduction or mechanical work transfer there has to be electromagnetic, photonic mass-energy propagation through involved material structures from a mass-energy source to a sink system. Steady-state, mass-energy transfer is depicted through heat conduction plate (at Figure top) and rotating shaft (at Figure bottom). Energy transfer (i.e., Einstein’s mass-energy equivalency transfer, ${\dot{E}}_{tr}={\dot{m}}_{tr}{c}^{2}$) has to be electromagnetic by photon transfer, either as photon electromagnetic waves on-long range through space/vacuum (${\dot{Q}}_{rad}={\dot{m}}_{rad}{c}^{2})$, or photon “on-contact” transfer (annihilation/reemission) within material structures, e.g., through heat conduction plate (at Figure top) and turbine shaft work (at Figure bottom), since it is neither gravitational nor nuclear (strong or weak) interaction. Otherwise, Einstein’s mass-energy equivalency and the fundamental force/interactions will be violated. Thermal conduction is due to chaotic thermal electron-shell collisions and may be enhanced by free-electrons or crystal-lattice structure vibration (phonons), both phenomena due to underlining photon propagation (similar to electro-chemical phenomena). The mechanical work transfer is due to electron-shell directional pushing/twisting as the most efficient (“focused”) energy transfer (i.e., mechanical super conductor). If it is fully investigated and understood, it has potential for development of hybrid synthetic-materials with superior thermal conductivity such as diamond and others, for critical and new applications [8].

**Figure 2.**Thermal and mechanical internal energies are distinguishable parts of the thermodynamic internal energy, the former increasing the thermal and the latter increasing the mechanical part of the internal energy, resulting in different states, regardless that the internal energies are the same, as illustrated by 1 kJ heating or 1 kJ compressing of ideal gas (

**A**), or a spring (

**B**).

**Figure 3.**During a spontaneous caloric heat transfer process between two thermal reservoirs, the work potential, W

_{Rev}, is completely dissipated into heat at a lower temperature, Q

_{Diss}, which after being added to the reduced reversible heat at lower temperature, Q

_{Rev}, will result in conserved heat or thermal energy, Q

_{Cal}= Q

_{Rev}+ Q

_{Diss}= constant, with increased, generated entropy in the amount of dissipated work potential per relevant absolute temperature [9,10].

**Figure 4.**Entropy is not a space disorder, nor form, nor functional disorder. Entropy is a thermal motion disorder. No thermal motion, no entropy! Expanding entropy to any type of disorder or information is a source of many misconceptions.

**Figure 5.**Maxwell’s demon (MD) operates its gate. MD opens the gate to “wishfully pass” a higher speed molecule from L to H (see dashed arrow line in L) and lower speed in reverse. However, considering the chaotic and fast, simultanious molecular thermal motion (most molecules are faster than sound speed), it is probable that the same or even higher speed molecule from H will pass back to L in that time period (or collide with an oncoming molecule, see dashed arrow line in H). Even higher speed molecules may pass back from H to L, and more probably so if MD was “successful by chance” to separate more high speed molecules into H. Therefore, “just opening the gate” would “more equalize than separate” by speed.

**Figure 6.**Destruction of entropy is impossible and cannot be “compensated” elsewhere or at later time. “Entropy of an isolated, closed system (or universe) is always increasing”, is a necessary but not sufficient condition of the Second Law of thermodynamics. Entropy cannot be destroyed, locally or at a time, and “compensated” by generation elsewhere or later. It would be equivalent to allow rivers to spontaneously flow uphill and compensate it by more downhill flow elsewhere or later. Entropy is generated everywhere and always, at any scale without exception, and cannot be destroyed by any means at any scale. Impossibility of entropy reduction by destruction should not be confused with local entropy decrease due to entropy outflow with heat [12].

**Figure 7.**Irreversible (solid lines) versus reversible process (dashed lines) towards mutual equilibrium. System A and B, each at constant volume, in thermal contact but isolated from the rest of surrounding.

**Figure 8.**Correlation between entransy G, reversible heat Q

_{REV}, entransy dissipation or loss G

_{LOSS}, and Carnot work-potential loss W

_{LOSS}, during 1-D steady-state heat conduction caloric process 1–2 with conserved heat transfer Q.

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**MDPI and ACS Style**

Kostic, M.M. Nature of Heat and Thermal Energy: From Caloric to Carnot’s Reflections, to Entropy, Exergy, Entransy and Beyond. *Entropy* **2018**, *20*, 584.
https://doi.org/10.3390/e20080584

**AMA Style**

Kostic MM. Nature of Heat and Thermal Energy: From Caloric to Carnot’s Reflections, to Entropy, Exergy, Entransy and Beyond. *Entropy*. 2018; 20(8):584.
https://doi.org/10.3390/e20080584

**Chicago/Turabian Style**

Kostic, Milivoje M. 2018. "Nature of Heat and Thermal Energy: From Caloric to Carnot’s Reflections, to Entropy, Exergy, Entransy and Beyond" *Entropy* 20, no. 8: 584.
https://doi.org/10.3390/e20080584