**6. Reply to criticisms of HTR**

The concept of HTR (without being dubbed HTR) was criticized by Makarieva, Gorshkov, Li, and Nobre [58] and by Bejan [59], as being in conflict with the First and Second Laws of Thermodynamics, especially with the Second Law (see especially Sections 4 and 5 of Ref. [58] and Section 4 of Ref. [59]). These criticisms are addressed directly in Ref. [60]. They are also addressed in works concerning (a) HTR in hurricanes [27–37, 62] and (b) the *experimental verification* of HTR in increasing efficiency of thermoelectric generators [38]. [Concerning (a) immediately above, on the one hand, the importance of HTR (dubbed as "dissipative heating") has been confirmed in a study of Hurricane Andrew (1992) [36], and, as one might expect, "dissipative heating appears to be a more important process in intense hurricanes, such as Andrew, than weak ones" [36]. But, on the other hand, more recently it has been contended [37] that, while HTR exists in hurricanes, it is of lesser importance than previously supposed [27–36].]

*Improving Heat-Engine Performance via High-Temperature Recharge DOI: http://dx.doi.org/10.5772/intechopen.89913*

and hence via HTR the engine's efficiency is increased from *W=QH* to

can *greatly* exceed the Carnot limit.

*Thermodynamics and Energy Engineering*

refractory material.

to do work is totally dissipated.

**6. Reply to criticisms of HTR**

**120**

lesser importance than previously supposed [27–36].]

*W=*ð Þ¼ *QH* � *W W=QC*, which can indeed exceed the Carnot limit—even though the efficiency *W=QH* of the *initial* production of work must be within the Carnot limit. If the temperature *TC* of the cold reservoir is only a small fraction of the the temperature *TH* of the hot reservoir, *W=QH* can be almost as large as unity or equivalently *W* can be almost as large as *QH*, and hence *W=*ð Þ¼ *QH* � *W W=QC*

We note that the temperature of the cosmic background radiation is only 2*:*7 K, while the most refractory materials remain solid at temperatures slightly exceeding 2700 K. This provides a temperature ratio of *RT* � *TC=TH* <sup>≈</sup> <sup>10</sup>�3. Could even smaller values of *RT* � *TC=TH* be possible, at least in principle? Perhaps, maybe, if frictional dissipation of work into heat might somehow be possible into a gaseous hot reservoir at temperatures exceeding the melting point or even the critical temperature (the maximum boiling point at any pressure) of even the most

While in this chapter we do not challenge the Second Law, we do challenge an *over*statement of the Second Law that is sometimes made: that energy can do work only once. This *over*statement is *false*. Energy can indeed do work more than once, in principle up to an infinite number of times, and even in practice many more times than merely once, before its ability to do work is totally dissipated. Consider these three examples: (i) Energy can do work in an infinite number of times in perfect (reversible) regenerative braking of an electrically-powered motor vehicle, with the motor operating backward as a generator during braking. Even with realworld less-than-perfect (less than completely reversible) regenerative braking, energy can do work many more times than merely once before its ability to do work is totally dissipated. (ii) Energy can do work in an infinite number of times in perfect (reversible) HTR (in the limit *RT* ! 0). Even with real-world less-thanperfect (less than completely reversible) HTR (finite but small *RT* >0), energy can do work many more times than merely once before its ability to do work is totally dissipated. (iii) Energy can do work in an infinite number of times in perfect (reversible) thermal recharge of intermediate heat reservoirs—not to be confused with HTR discussed in this present chapter—see Section VI of Ref. [35] and the improved treatment in another chapter [61] in this book. Even with real-world lessthan-perfect (less than completely reversible) thermal recharge of intermediate heat reservoirs, energy can do work more times than merely once before its ability

The concept of HTR (without being dubbed HTR) was criticized by Makarieva, Gorshkov, Li, and Nobre [58] and by Bejan [59], as being in conflict with the First and Second Laws of Thermodynamics, especially with the Second Law (see especially Sections 4 and 5 of Ref. [58] and Section 4 of Ref. [59]). These criticisms are addressed directly in Ref. [60]. They are also addressed in works concerning (a) HTR in hurricanes [27–37, 62] and (b) the *experimental verification* of HTR in increasing efficiency of thermoelectric generators [38]. [Concerning (a) immediately above, on the one hand, the importance of HTR (dubbed as "dissipative heating") has been confirmed in a study of Hurricane Andrew (1992) [36], and, as one might expect, "dissipative heating appears to be a more important process in intense hurricanes, such as Andrew, than weak ones" [36]. But, on the other hand, more recently it has been contended [37] that, while HTR exists in hurricanes, it is of

Perhaps the simplest and most straightforward reply to these criticisms [58, 59] is that provided by Spanner (see Ref. [6], pp. 11–12, 60–65, and 263–265, especially pp. 263–265): Friction resulting from dissipation of work can in principle generate arbitrarily high temperature *TH* without violating the Second Law of Thermodynamics: The entropy increase resulting from frictional dissipation of work *W* at temperature *TH*, namely, Δ*S* ¼ *W=TH*, decreases monotonically with increasing *TH* but is positive for any finite *TH*—and the Second Law requires only that Δ*S*≥ 0 [6]. A heat engine operating between this high temperature *TH* and a low (cold-reservoir) temperature *TC* arbitrarily close to absolute zero (0 K) can in principle recover essentially all of the frictional dissipation as work [6]—and the recycling of energy from work to heat via frictional dissipation and then back to work via the heat engine can in principle then be repeated essentially indefinitely [6]. No energy is created (or destroyed)—energy is merely recycled—hence the First Law of Thermodynamics is not violated [6]. No decrease in entropy occurs—Δ*S* ¼ *W=TH* >0 for any finite *TH* hence the Second Law of Thermodynamics is not violated [6].

As has been previously emphasized [35], it is only recycling of a heat engine's *waste heat QC* into its hot reservoir at *TH* instead of rejection thereof into its cold reservoir at *TC*—*not* recycling of heat generated by frictional dissipation of its *work output W* back into its hot reservoir at *TH*—that would violate the Second Law of Thermodynamics. Recharging *W* to the hot reservoir does *not* violate the Second Law, because the entropy change Δ*S* ¼ *W=TH* is positive—albeit less strongly positive than Δ*S* ¼ *W=TC* that obtains if *W* is frictionally dissipated into the cold reservoir. Only recharging *QC* to the hot reservoir would violate the Second Law, because the entropy change Δ*S* ¼ *QC=TH* � *QC=TC* would be negative. And recycling of a heat engine's *waste heat QC* into its hot reservoir at *TH* instead of its rejection into its cold reservoir at *TC* has *never* been claimed [27–38, 60, 62].

There is one caveat: the entropy increase Δ*S* ¼ *W=TH* > 0 owing to frictional dissipation of *W* at *TH* could in principle be employed to pay for pumping a heat engine's waste heat *QC* from *TC* to *TH*, but no capability to do work would be gained by this procedure. For, even if this procedure could be executed perfectly (reversibly), e.g., via a perfect (reversible) heat pump, we would have [applying Eqs. (1) and (5)]

$$
\Delta \mathbf{S}\_{\text{total}} = \frac{W}{T\_H} - \frac{\mathbf{Q}\_C}{T\_C} + \frac{\mathbf{Q}\_C}{T\_H} = \frac{W}{T\_H} - \mathbf{Q}\_C \left(\frac{1}{T\_C} - \frac{1}{T\_H}\right) = \frac{W}{T\_H} - \mathbf{Q}\_C \frac{T\_H - T\_C}{T\_C T\_H} = \mathbf{0}
$$

$$
\Rightarrow W = \mathbf{Q}\_C \frac{T\_H - T\_C}{T\_C} = \mathbf{Q}\_C \left(\frac{T\_H}{T\_C} - 1\right) = \mathbf{Q}\_H \frac{T\_C}{T\_H} \left(\frac{T\_H}{T\_C} - 1\right) \tag{22}
$$

$$
= \mathbf{Q}\_H \left(\mathbf{1} - \frac{T\_C}{T\_H}\right) = \mathbf{Q}\_H (\mathbf{1} - \mathbf{R}\_T) = \mathbf{Q}\_H \mathbf{e\_{Carnot, std}}
$$

What Eq. (22) brings to light is that the operation of the heat pump, even if perfect (reversible), results merely in the recovery of *W*. But *W* is recoverable more simply by avoiding this unnecessary procedure, as per Section 5 and the first three paragraphs of this Section 6.

### **7. Conclusion**

We provided introductory remarks, an overview, and general considerations in Section 1. A misconception pertaining to the efficiencies of engines (heat engines or otherwise) was discussed and corrected in Section 2. Then we discussed the work outputs, efficiencies, and entropy productions of Carnot (reversible) and Curzon-Ahlborn (endoreversible) heat engines. In Section 3, we reviewed the standard (without HTR) work outputs, efficiencies, and entropy productions of Carnot (reversible) and Curzon-Ahlborn (endoreversible) heat engines, first without frictional dissipation of heat engines' work outputs and then with frictional dissipation thereof into their cold reservoirs. In Section 4 we considered them with frictional dissipation of heat engines' work outputs into their hot reservoirs (with HTR). (If HTR is employed, we construe the terms "the highest practicable temperature for HTR" and "the hot reservoir" to be synonymous.) We showed that the efficiencies of both Carnot and Curzon-Ahlborn engines can be increased, indeed in some cases greatly increased, via employing HTR. The increases in efficiencies via employing HTR are minimal in the limit *RT* � *TC=TH* ! 1 but become arbitrarily large in the limit *RT* � *TC=TH* ! 0. Efficiencies via employing HTR can exceed unity and can even approach ∞.

frictionally dissipated heat into work, and hence improved cyclic heat-engine per-

violated. The First Law is not violated because no new energy is created (or destroyed): super-unity efficiencies via employment of HTR obtain via recycling and reusing the same energy, not via the creation of new energy. The Second Law is not violated because the change in total entropy is positive if HTR is employed and frictional dissipation of work as heat is into the hot reservoir, albeit less strongly positive than if HTR is not employed and frictional dissipation of work as heat is into the cold reservoir. The improved heat-engine performance that HTR provides

associated with the energy-time uncertainty principle [73, 74]. But there are

I am very grateful to Dr. Donald H. Kobe, Dr. Paolo Grigolini, Dr. Daniel P. Sheehan, Dr. Bruce N. Miller, and Dr. Marlan O. Scully and for many very helpful and thoughtful insights, as well as for very perceptive and valuable discussions and communications, that greatly helped my understanding of thermodynamics and statistical mechanics. Also, I am indebted to them, as well as to Dr. Bright Lowry, Dr. John Banewicz, Dr. Bruno J. Zwolinski, Dr. Roland E. Allen, Dr. Abraham Clearfield, Dr. Russell Larsen, Dr. James H. Cooke, Dr. Wolfgang Rindler, Dr. Richard McFee, Dr. Nolan Massey, and Dr. Stan Czamanski for lectures, discussions, and/or communications from which I learned very much concerning thermodynamics and statistical mechanics. I thank Dr. Stan Czamanski and Dr. S. Mort Zimmerman for very interesting general scientific discussions over many years. I also thank Dan Zimmerman, Dr. Kurt W. Hess, and Robert H. Shelton for very interesting general scientific discussions at times. Additionally, I thank Robert H.

ultimately obtains from this reduction of entropy increase.

*Improving Heat-Engine Performance via High-Temperature Recharge*

contrasting viewpoints [73, 74] concerning the latter issue.

Shelton for very helpful advice concerning diction.

The author declares no conflicts of interest.

We emphasize yet again that First and Second Laws of Thermodynamics are *not*

While in this chapter we do not challenge the First or Second Laws of Thermodynamics, we should note that there have been many challenges to the Second Law, especially in recent years [64–69]. By contrast, the First Law has been questioned only in cosmological contexts [70–72] and with respect to fleeting violations thereof

formance, can then obtain.

*DOI: http://dx.doi.org/10.5772/intechopen.89913*

**Acknowledgements**

**Conflicts of interest**

**123**

We provided recapitulation, as well as generalization, in Section 5. We replied to criticisms [58, 59] of HTR in Section 6.

As we have already noted in Section 1, the increases in efficiency attainable via HTR are not practicable if frictional dissipation of work into other than the cold reservoir is not practicable. Thus they are *never* practicable for noncyclic (necessarily one-time, single-use) heat engines: however the work output of a noncyclic (necessarily one-time, single-use) heat engine might be frictionally dissipated, the heat thereby generated can*not* restore the engine to its initial state. Moreover in many cases the work outputs of noncyclic (necessarily one-time, single-use) heat engines are not frictionally dissipated *at all*, at least not during practicable time scales, for example, a noncyclic rocket heat engine's work output is sequestered essentially permanently as kinetic and gravitational potential energy in the launching of a spacecraft (but typically most of the kinetic energy accelerates the exhaust gases, not the payload). They also are *never* practicable for reverse operation of cyclic heat engines as refrigerators or heat pumps, because for both refrigerators and heat pumps, the *total* energy input (the work *W*, plus the heat *QC* extracted from a cold reservoir at the expense of *W* as required by the Second Law of Thermodynamics) *always* is deposited as heat *QH* into a hot reservoir (*QH* ¼ *QC* þ *W*): thus there is *never* any *additional* energy to be deposited into the hot reservoir (as there is from frictional dissipation of work done via forward operation of cyclic heat engines). {See Ref. [1], Section 20-3; Ref. [2], Sections 4.3, 4.4, and 4.7 (especially Section 4.7); Ref. [3], Sections 4-4, 4-5, and 4-6 (especially Section 4-6); Ref. [5], Section 5.12 and Problem 5.22; Ref. [7], pp. 233–236 and Problems 1, 2, 4, 6, and 7 of Chapter 8; Ref. [16], Chapter XXI; Ref. [17], Sections 6.7, 6.8, 7.3, and 7.4; and Ref. [54], Sections 5-7-2, 6-2-2, 6-9-2, and 6-9-3, and Chapter 17. [Problem 2 of Chapter 8 in Ref. [7] considers absorption refrigeration, wherein the entire energy output is into an *intermediate*-temperature (most typically ambient-temperature) reservoir, and hence for which HTR is *even more strongly never practicable.*]} They also are not practicable for cyclic heat engines in cases wherein a cyclic heat engine's work output is not frictionally dissipated immediately or on short time scales [16, 17], for example, as gravitational potential energy sequestered for a long time interval in the construction of a building. For a building once erected typically remains standing for a century or longer. Even if, when it is finally torn down, its gravitational potential energy were to be totally frictionally dissipated into a hot reservoir, it is simply impracticable to wait that long. Thus HTR is not practicable in all cases. But in the many cases wherein cyclic heat engines' work outputs are frictionally dissipated immediately or on short time scales [16, 17], practicability obtains: improved conversion—and reconversion—of

*Improving Heat-Engine Performance via High-Temperature Recharge DOI: http://dx.doi.org/10.5772/intechopen.89913*

frictionally dissipated heat into work, and hence improved cyclic heat-engine performance, can then obtain.

We emphasize yet again that First and Second Laws of Thermodynamics are *not* violated. The First Law is not violated because no new energy is created (or destroyed): super-unity efficiencies via employment of HTR obtain via recycling and reusing the same energy, not via the creation of new energy. The Second Law is not violated because the change in total entropy is positive if HTR is employed and frictional dissipation of work as heat is into the hot reservoir, albeit less strongly positive than if HTR is not employed and frictional dissipation of work as heat is into the cold reservoir. The improved heat-engine performance that HTR provides ultimately obtains from this reduction of entropy increase.

While in this chapter we do not challenge the First or Second Laws of Thermodynamics, we should note that there have been many challenges to the Second Law, especially in recent years [64–69]. By contrast, the First Law has been questioned only in cosmological contexts [70–72] and with respect to fleeting violations thereof associated with the energy-time uncertainty principle [73, 74]. But there are contrasting viewpoints [73, 74] concerning the latter issue.

### **Acknowledgements**

otherwise) was discussed and corrected in Section 2. Then we discussed the work outputs, efficiencies, and entropy productions of Carnot (reversible) and Curzon-Ahlborn (endoreversible) heat engines. In Section 3, we reviewed the standard (without HTR) work outputs, efficiencies, and entropy productions of Carnot (reversible) and Curzon-Ahlborn (endoreversible) heat engines, first without frictional dissipation of heat engines' work outputs and then with frictional dissipation thereof into their cold reservoirs. In Section 4 we considered them with frictional dissipation of heat engines' work outputs into their hot reservoirs (with HTR). (If HTR is employed, we construe the terms "the highest practicable temperature for HTR" and "the hot reservoir" to be synonymous.) We showed that the efficiencies of both Carnot and Curzon-Ahlborn engines can be increased, indeed in some cases greatly increased, via employing HTR. The increases in efficiencies via employing HTR are minimal in the limit *RT* � *TC=TH* ! 1 but become arbitrarily large in the limit *RT* � *TC=TH* ! 0. Efficiencies via employing HTR can exceed unity and can

We provided recapitulation, as well as generalization, in Section 5. We replied to

As we have already noted in Section 1, the increases in efficiency attainable via HTR are not practicable if frictional dissipation of work into other than the cold reservoir is not practicable. Thus they are *never* practicable for noncyclic (necessarily one-time, single-use) heat engines: however the work output of a noncyclic (necessarily one-time, single-use) heat engine might be frictionally dissipated, the heat thereby generated can*not* restore the engine to its initial state. Moreover in many cases the work outputs of noncyclic (necessarily one-time, single-use) heat engines are not frictionally dissipated *at all*, at least not during practicable time scales, for example, a noncyclic rocket heat engine's work output is sequestered essentially permanently as kinetic and gravitational potential energy in the launching of a spacecraft (but typically most of the kinetic energy accelerates the exhaust gases, not the payload). They also are *never* practicable for reverse operation of cyclic heat engines as refrigerators or heat pumps, because for both refrigerators and heat pumps, the *total* energy input (the work *W*, plus the heat *QC* extracted from a cold reservoir at the expense of *W* as required by the Second Law

of Thermodynamics) *always* is deposited as heat *QH* into a hot reservoir

(*QH* ¼ *QC* þ *W*): thus there is *never* any *additional* energy to be deposited into the hot reservoir (as there is from frictional dissipation of work done via forward operation of cyclic heat engines). {See Ref. [1], Section 20-3; Ref. [2], Sections 4.3, 4.4, and 4.7 (especially Section 4.7); Ref. [3], Sections 4-4, 4-5, and 4-6 (especially Section 4-6); Ref. [5], Section 5.12 and Problem 5.22; Ref. [7], pp. 233–236 and Problems 1, 2, 4, 6, and 7 of Chapter 8; Ref. [16], Chapter XXI; Ref. [17], Sections 6.7, 6.8, 7.3, and 7.4; and Ref. [54], Sections 5-7-2, 6-2-2, 6-9-2, and 6-9-3, and Chapter 17. [Problem 2 of Chapter 8 in Ref. [7] considers absorption refrigeration, wherein the entire energy output is into an *intermediate*-temperature (most typically ambient-temperature) reservoir, and hence for which HTR is *even more strongly never practicable.*]} They also are not practicable for cyclic heat engines in cases wherein a cyclic heat engine's work output is not frictionally dissipated immediately or on short time scales [16, 17], for example, as gravitational potential energy sequestered for a long time interval in the construction of a building. For a building once erected typically remains standing for a century or longer. Even if, when it is finally torn down, its gravitational potential energy were to be totally frictionally dissipated into a hot reservoir, it is simply impracticable to wait that long. Thus HTR is not practicable in all cases. But in the many cases wherein cyclic heat engines' work outputs are frictionally dissipated immediately or on short time scales [16, 17], practicability obtains: improved conversion—and reconversion—of

even approach ∞.

**122**

criticisms [58, 59] of HTR in Section 6.

*Thermodynamics and Energy Engineering*

I am very grateful to Dr. Donald H. Kobe, Dr. Paolo Grigolini, Dr. Daniel P. Sheehan, Dr. Bruce N. Miller, and Dr. Marlan O. Scully and for many very helpful and thoughtful insights, as well as for very perceptive and valuable discussions and communications, that greatly helped my understanding of thermodynamics and statistical mechanics. Also, I am indebted to them, as well as to Dr. Bright Lowry, Dr. John Banewicz, Dr. Bruno J. Zwolinski, Dr. Roland E. Allen, Dr. Abraham Clearfield, Dr. Russell Larsen, Dr. James H. Cooke, Dr. Wolfgang Rindler, Dr. Richard McFee, Dr. Nolan Massey, and Dr. Stan Czamanski for lectures, discussions, and/or communications from which I learned very much concerning thermodynamics and statistical mechanics. I thank Dr. Stan Czamanski and Dr. S. Mort Zimmerman for very interesting general scientific discussions over many years. I also thank Dan Zimmerman, Dr. Kurt W. Hess, and Robert H. Shelton for very interesting general scientific discussions at times. Additionally, I thank Robert H. Shelton for very helpful advice concerning diction.

### **Conflicts of interest**

The author declares no conflicts of interest.

*Thermodynamics and Energy Engineering*

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*DOI: http://dx.doi.org/10.5772/intechopen.89913*

*Improving Heat-Engine Performance via High-Temperature Recharge*

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