So far in looking at the broad topic of efficiency, we’ve focused on what I described in the introductory post as the analytic perspective. In this post I’ll start to consider the systemic view of efficiency in more detail, by taking a closer look at the concept of available energy: the maximum work output achievable when a system is brought into equilibrium with its environment (or, as the corollary of this, the minimum work input required to bring about a given change in a system’s state).

Origins and subsequent developments

The available energy concept was first introduced to the science of thermodynamics by Josiah Willard Gibbs in 1873.[1] In the 1940s and 50s, Joseph Keenan extended Gibbs’s available energy for engineering applications as availability, adapting it for the practical analysis of thermodynamic cycles, especially for power generation and refrigeration.[2] In doing so, Keenan established the basis for determining the maximum useful work output from a system of fixed mass (a “control mass”), and also extended this to systems involving a constant throughput of matter, such as internal combustion engines. The latter class of systems are treated in engineering thermodynamics via the method known as control volume analysis, for which Keenan also played an instrumental role in the development. Control volume analysis allows the thermodynamic techniques originally formulated for systems comprising a fixed mass (“closed systems”, in engineering thermodynamics) to be extended to systems in which the component mass is undergoing constant or intermittent exchange with the system’s environment (“open systems”). In other words, while available energy is typically described as the maximum work output when a system undergoes a change in state that brings it into equilibrium with its environment, this also covers situations in which the matter flowing through a designated space reaches equilibrium with the surrounds, while the physical components that delineate that space—for example, the components that bound the interior surface of an engine from air intake, to cylinders and pistons, to exhaust—remain out of equilibrium with the surrounds (in practical terms, this means that the temperature of the engine’s components is elevated relative to the surrounds). The situations to which control volume analysis can be applied include machines of all types that involve conversions of heat and work, but also extend in principle to organisms.[8]

Terminology: the advent of exergy

In parallel with Keenan’s development of availability analysis for applications in engineering thermodynamics (i.e. for processes involving energy conversions), similar developments were occurring in Europe and Russia for both energy conversion and chemical processing applications.[3] In 1953, Zoran Rant proposed the term exergy for a system’s maximum work capacity, and this was formally introduced in a 1956 publication.[4] Over subsequent decades, exergy has gradually come to be accepted as the default term, and today has largely replaced availability and available energy in most contexts worldwide. This is simply a matter of convention though: exergy and availability (in its thermodynamic sense) are entirely synonymous with one another, and in fact the terms do continue to be used together, or interchangeably. For instance, the most recent edition of the engineering thermodynamics text that was the basis for my own undergraduate studies, Borgnakke and Sonntag’s Fundamentals of Thermodynamics (2008, 7^th edition, Wiley, New York), refers to available energy, availability and exergy. Exergy is the new comer here: in the earlier edition with which I’m most familiar (Van Wylen, G and Sonntag, R, 1985, Fundamentals of Classical Thermodynamics, 3^rd ed, John Wiley & Sons, New York), all discussion on this topic is in terms of availability. Even so, for simple expediency and given that the long-term trend towards standardisation seems to be converging here also, from here on I’ll mainly stick to using the term exergy.

Preliminary reflections on the utility of the exergy concept and its limits

Whereas the total energy of a system is a property of the system alone (or a little more specifically, is defined in relation to a frame of reference local to the system itself), the exergy associated with a system is a property of the system considered in relation to its surrounds. That is, it depends on the system’s context. A theme frequently discussed at Beyond this Brief Anomaly is the very abstract nature of the energy concept—when we characterise a situation in which we’re interested exclusively in energy terms, we’re losing just about as much of the nuance of that situation as is possible while still saying something at all. In this respect, characterising a situation in terms of exergy is a little less abstract—but only a little. I highlight this point, because a guiding interest for this series of posts on efficiency-related matters is the limited utility of comparing or aggregating different energy sources on the basis of their nominal heating values alone. Doing so obscures from view the myriad contextual considerations that must be taken into account in understanding the value of an energy source—including those that directly impact on how much work, heating or lighting we can get a given source to do for us. In this respect, exergy analysis may appear to offer a ready-made pathway for addressing the problems that arise with the convention of characterising energy sources solely in terms of the gross energy quantity they provide. As it turns out, this is indeed one of the major application areas to which proponents for exergy analysis have turned their attention. Exergy-based analytical approaches have for a long while now been proposed as a means of making quality-related corrections to the nominal energy value of energy sources. So before I get too far along here, I’d like to point out that my purpose in discussing exergy here is not to advocate for such an approach. In fact, one of the tasks I’d like to attempt as we proceed, here and in subsequent posts, is to set out the broader case for why such efforts may be misguided. I’ll do this under a wider umbrella though: this relates to the use of narrowly applicable concepts, including exergy, for deriving quantitative measures of “sustainability” more broadly.

A general observation guiding this is that our conceptual constructs—that is, the mental and cultural tools that we develop to make sense of the situations in which we’re interested and to negotiate their meaning with one another—are very often good servants, but tend to be pretty poor masters. That servant concepts do often exhibit a kind of psycho-cultural “social mobility” in which their status is elevanted from tools that we use at our discretion, to frameworks within which our thinking can become constrained (or put another way, from ideas we hold to ideas that hold us), relates in part to the process of reification that I’ve mentioned on more than one occasion as the inquiry has unfolded. This reification involves concepts taking on a life of their own, almost literally, as they move beyond their originating context and are increasingly assumed to deal with features of reality having an inherent existence independent of us. I’ve previously highlighted the way that the energy concept itself is open to such transformation—in many respects, it’s typical of any idea that takes hold in the wider human imagination, and to draw on a metaphor from biological evolution, in purely reproductive terms could be viewed as a measure of an idea’s success. The more abstract—and in a related sense, the more subtle—is the original idea though, the more significant are the opportunities for unhelpful distortions to creep in. An idea that once provided its skilled users with mental clarity, dexterity and power becomes in hands trained in ways less commensurate with the original intent a potential source of confusion. For those of us who, by virtue of being trained insufficiently in an idea’s use to make our own discernments, must take its various applications both orthodox or heterodox as being at face value consistent with use that the originators would recognise as skilled, the pitfalls of reification require constant vigilance. Later in this post, I’ll give some attention to how all this plays out in relation to exergy. Before doing that though, I’ll give some closer attention to what I see as the particularly important strengths and benefits of an exergy-based approach in the context of the wider efficiency theme.

Applications

Roughly speaking, applications of the exergy concept divide into two broad categories: i) systems analysis; and ii) characterisation of material properties. The latter category includes resource valuation, including “resources” that tend to be regarded as having negative value i.e. wastes associated with detrimental impacts (although this can be relative to one’s particular point of view—as implied by the folk saying “one man’s waste is another’s treasure”); it’s this area that I’ll focus on later in addressing the issues discussed in the previous section. The important contributions of the exergy concept that we’ll look at beforehand relate to the first category. Exergy “systems analysis” today covers a much broader spectrum of applications than its originators may have envisaged. Originally, it applied to energy conversions and chemical processing—that is, to systems from the scale of individual devices up to industrial plant scale. These are the most mature and, it’s probably fair to say, most immediately valuable applications in a practical sense. They are also the least contentious—they’re founded on well-established and fundamental thermodynamic principles, and are most readily subject to validation. They may also lead directly to tangible performance improvements, often measurable in terms of capital and operating cost benefits. More recently, this has been extended to analysis of economic, biological and social systems, and to life-cycle assessment.[3] It’s the more conventional applications of exergy analysis that I want to focus on, perhaps reflecting my own background in engineering thermodynamics—after all, I’m most familiar with the exergy concept, as availability, in this context. This is also far and away where the majority of its practical contributions can be found.

Making sense of exergy: how can this advance the inquiry?

The guiding idea that I want to draw out here is that in order to understand the economic value of an energy source, we need to take into account the context of its use i.e. the way in which the energy associated with it is converted to a form useful to us. We started to look at this in the earlier post on analytic perspectives on efficiency, by considering how the designs of our energy conversion systems—the specific technologies and infrastructures—affect the proportion of the energy nominally associated with an energy source that actually does what we want it to do—for example, illuminating or heating living spaces, moving us from place to place or transforming the composition and shape of materials. The extension to this that exergy analysis provides is to explicitly take into account the environmental context of our energy conversion systems in determining their capacity to effect change in their surrounds through carrying out work, transferring heat or by any other means. This recognises that changing environmental context affects the amount of work that a system can do on its surrounds. Take for instance a thermodynamic system—say a quantity of steam—at a given temperature and pressure. Such a system can be characterised in terms of its internal energy—the total thermal and mechanical energy of the steam, relative to an appropriate frame of reference for temperature and pressure. While knowing the system’s (locally defined) temperature and pressure allows for its characterisation in energy terms—i.e. we know how much internal energy is associated with it—on its own this tells us nothing about the quantity of work that the system can do on its surrounds. In order to know this, we need to know the relative difference in temperature and pressure between the system and its surrounds; variations in these relative differences will affect the work that the system can do. The maximum useful work that the system can do is that which would bring the system into equilibrium with its surrounds, reversibly (i.e. without any losses). This is the availability or exergy of the system in combination with its surrounds. (Note that this is measured in the same units as energy and work—in the SI system, joules (J)). The actual useful work that the system can do on the surrounds must be less than or equal to this exergy value (it will be less for all real processes which inevitably entail various losses, or “irreversibilities”). For any given system, if the temperature (or pressure) of the surrounding environment increases, the exergy will decrease, and vice versa for decreases in temperature or pressure of surrounds. In practice, this means that for a particular energy source and energy conversion technology—say for instance a quantity of diesel fuel of particular composition and a particular compression-ignition engine—where (or when) it is operating will affect the amount of work that can be obtained from the fuel. This is most notable in relation to temperature differences, either between summer and winter for a particular location, or between locations with different climates. Given that the annual variation between winter minimum and summer maximum temperatures for a location can vary by as much as 80^oC (from -40 ^oC to +40 ^oC for example in some places in North America and elsewhere), in principal this can make for a significant range (though in practice, other temperature-related performance differences will come into play and may mean that the system’s overall efficiency also changes with ambient temperature—actual winter-to-summer performance differences may diverge from the theoretical exergy difference). Note 1

In the example above, I’ve specifically looked at the case of a system in which the principal contribution to the total energy is the internal energy i.e. where total energy is comprised of thermal and mechanical energy. All forms of energy—including chemical, electrical, gravitational, elastic, magnetic and so on—are relevant though and contribute to the system’s total energy. Where ever there is a difference between a system’s potential and that of its surrounding environment for the particular forms of energy associated with that system, there is scope for the system to do work on its environment. So for instance, if there is a difference in electrical potential (i.e. if the system is at a higher voltage than its surrounds), then the system can do electrical work; similarly for differences in chemical potential, and so on. These potential differences are effectively differences in energy concentration between the system and surrounds, for each of the physical phenomena with which the system’s energy is associated. For those who’ve been following for a while now, this description of exergy in terms of relative energy concentrations may be reminiscent of the outline that I provided early on of the physical behaviour with which the second law of thermodynamics is associated—in brief form “energy tends to disperse from where it is more concentrated to where it is more spread out, unless hindered from doing so”. This is no coincidence: the exergy for a system in a given context—the maximum work that the system can do on its surrounds—arises directly from the propensity described by the second law. It is this tendency for more concentrated energy to disperse that “enables” all work (or for that matter, that “allows” all happenings everywhere). Moreover, the relationship between exergy and energy follows directly from the insights by which the second law of thermodynamics extends the first law: while energy cannot be consumed or “used up” (first law: energy is simply converted from one form to another), it’s utility for doing work is “used up” (second law: energy disperses from where it’s more concentrated—and hence more available—to less concentrated, and hence less available). It is the energy’s utility for doing work that the exergy measures. Whereas energy is not “consumed” or “destroyed” when it is used, exergy is consumed or destroyed.

The exergy associated with a system in a given context is a function of the quantity of each form of energy associated with the system, and the relative differences in energy concentrations between the system and its immediately surrounding environment. A system can have a relatively large quantity of energy associated with it, but very little exergy (and therefore very little capacity to do useful work), when it is close to its “dead state”—the state in which it is in equilibrium with its surrounds. On the other hand, a system may have a relatively smaller quantity of energy associated with it, but a relatively larger exergy value (and correspondingly larger capacity to do useful work), due to that energy being highly concentrated compared with the surrounds. Imagine, for example, a very large pressure vessel containing air at ambient pressure and temperature. The vessel’s internal energy is not zero, however its exergy will be close to zero. Compare this with a much smaller vessel containing air at pressure higher than ambient, and at ambient temperature. Even though the internal energy may be similar to—or, depending on the relative quantities of air contained in the two vessels, even less than—that of the larger vessel, its exergy will be higher. Or take another example in which two equal quantities of a fuel are burned to heat two different quantities of water, generating steam to drive identical turbines. For the system containing the smaller quantity of water, a correspondingly smaller quantity of steam is generated than for the system containing the larger quantity of water, but the steam is at a higher temperature than that of the larger system. For which of these systems will the turbine’s work output be larger? Overlooking for now some possible differences in the heat transfer process due to the steam temperature, the internal energy of each system is nominally the same, so this won’t help answer our question. To make this assessment, we need to calculate the exergy for each system. These examples will hopefully illustrate the utility of the exergy concept—and demonstrate how it is in important respects a less abstract concept than a system’s energy: it tells us more about what a system can do under prevailing circumstances, by explicitly taking those circumstances into account.

Second law efficiency

One of the most important contributions of exergy analysis is enabling the calculation of what is known as second law efficiency. For most day-to-day purposes the energy efficiency of a device or process is calculated in terms of the net useful energy output, and the heat input, often simply via the nominal heating value of the fuel input. While this allows for comparing relative performance between devices or processes, or for comparing a particular device or process at different times, it provides us with only a notional performance index rather than a specific measure of actual performance relative to theoretical ideal performance. The second law efficiency provides such a measure—it allows engineers to assess how closely plant and equipment approaches what we could call “thermodynamic perfection”, by directly evaluating the irreversibility associated with an energy conversion process. As discussed previously, irreversibilities correspond with all of the ways in which real processes depart from ideal behaviour, reducing useful work output in the case of power generation or increasing the work input required to carry out a desired physical function. These include mechanical losses due to friction or turbulence, electrical resistance and so on. To appreciate the utility of the second law efficiency, we can consider a process such as the generation of shaft power from a gas turbine. If we know the actual work output from the turbine, and the actual combustion gas inlet and outlet states (e.g. we know both the temperature and pressure at the inlet and at the outlet), then we can calculate the change in the exergy from inlet to outlet state and compare this with the actual work output. The difference between the actual work output and the change in exergy is the irreversibility for the process; it tells us how close we are to the ideal situation in which the change in state is entirely accounted for by useful work output. This has great utility for monitoring machine performance, and in assessing potential for design improvements.

Moreover, second law efficiency provides a measure of how well we are doing in regard to resource utilisation—exergy loss due to irreversibilities represents, at least in principle, the degree to which an energy resource can be viewed as under-utilised. If the work output from an energy conversion process is less than the change in exergy that would bring the system into equilibrium with its surrounding environment—as it is in all real situations—then this means that some residual exergy is lost to that environment. In colloquial terms, it is wasted—but there is another important implication of this too. The residual exergy has the potential to, and in practice typically does, effect significant and measurable changes on that environment. For power generation processes, the most notable way that this plays out is through slightly elevated temperature in the surrounds. But where the residual exergy is associated with a chemical potential—for example: in power generation, via incompletely combusted fuel; in chemical processing, via residual reactants or waste products that can undergo further reactions in the surrounding environment; or via nutrients on which organisms can feed—then other possibly detrimental impacts can result. In other words, the impacts associated with many environmental pollutants can be linked with their residual exergy (though as we’ll see in a moment, this does not mean that exergy provides a direct measure of this environmental impact—just that there may in some instances be a relationship here).

Exergy, resource characterisation and sustainability indicators

Earlier I noted a second significant area to which exergy analysis is now applied, extending the concept beyond its origins in energy conversion and chemical processing systems analysis. As I alluded to there, applications in this area should be approached with some considerable caution. In its broadest sense, this second area of application relates to the characterisation of material properties in exergy terms, but it is a subset of this work, dealing with resource valuation (including “negative” resources, or wastes capable of detrimental impacts), on which I want to focus. The use of exergy analysis for this purpose has received particular attention under the rubric of sustainability.

At face value, exergy analysis appears to offer a rather neat and convenient basis for developing quantitative, scientifically rigorous measures of “sustainability”. For instance, on such grounds a claim might be made that a particular power generation process delivering a given quantity of electricity at lower overall exergy consumption than another process is therefore “more sustainable” than the alternative. Such claims typically rest on efficiency-based arguments—in short, that it is better (“more sustainable”) to consume less exergy for a given desired function than it is to consume more; or conversely, that for a given exergy consumption, it is better (“more sustainable”) to get more of a desired function than less.

Numerous caveats make such use of exergy analysis far less straightforward than they appear on first inspection. These include:

• that efficiency-based approaches to sustainability assessment carry with them important contextual implications that require close scrutiny (we’ll start to look at these in a couple of posts, under the topic of rebound effects);
• the extent to which other important criteria not measurable in exergy terms might be discounted or overlooked if this approach is taken too far; and
• that the importance of taking full life-cycle considerations into account in making such quantitative assessments tends to make approaches such as these far less “neat and convenient” than they appear on the surface (dealing with this raises issues of boundary contestation, that mean such analyses are never simply technical matters, but must also involve negotiating meanings in the social domain—more on this when we take a deeper look at EROI in the next post).

Even so, and interpretive dilemmas aside, efforts such as these are based at least on valid use of the exergy concept—use that is consistent with the concept’s original thermodynamic foundations, and the associated analytical techniques. Approached judiciously, work of this nature clearly has an important role to play in sustainability-related evaluation and decision making.  Exergy-based resource quality and waste impact evaluation rests on much shakier ground.

That exergy analysis is in fact widely proposed as a basis for measuring resource value and environmental impact is readily established by a quick perusal of the literature on both exergy analysis and sustainability. This article by Koroneos, Nanaki and Xydis is illustrative [6], and also highlights another important distinction that must be made in this area. The distinction relates specifically to the measurement of resource value in exergy terms. There are two fundamentally different senses in which we can think of this. The first relates to the embodied exergy of secondary resources such as manufactured materials i.e. materials that have required the consumption of exergy in their production. Provided that calculation of the exergy consumption is based on appropriate analysis of the particular energy conversion systems involved in the full manufacturing process from production of raw materials to supply of finished products, then this may provide a valid and useful valuation of the material as a resource in real economic terms. This is quite distinct from the second sense in which exergy-based resource valuation is used.

The second sense involves the attribution of exergy quantities to materials as a measure of their thermodynamic potential i.e. their potential for providing work (in the case of power generation) or process heat input (mainly for chemical processing e.g. an exergy value might be attributed to copper concentrate, the oxidation of which provides most of the process heat for smelting to produce copper matte). In contrast with the first embodied exergy resource valuation sense, this second sense is highly problematic. Exergy is a property of a thermodynamic system in combination with a specific reference environment. To calculate an exergy value, an appropriate system must be defined, in the context of a particular reference environment. In other words, exergy values are situation-specific. Exergy is not an intrinsic property of objects or materials in isolation; and like energy, it is certainly not an inherently existent “thing” contained within a quantity of material. For instance, the work that a fuel can make available is dependent on the chemical composition of the fuel, the specific power generation cycle involved, the way that the cycle is practically implemented (i.e. the actual equipment involved) and the environment in which the power generation system operates. A whole raft of considerations make the attribution of exergy values to materials such as fossil energy sources on the basis of their chemical composition alone a very dubious undertaking. This also means that embodied exergy calculations that use such exergy values as their basis (rather than system-specific exergy values for the actual energy conversion processes involved in the manufacture of the goods or services we’re interested in) will be of similarly questionable value.

Exergy-based valuation has also been proposed widely for valuing non-energy resources. These run into a raft of additional problems, not least of which is the issue of whether exergy actually has any relevance as a measure of value for purposes other than those that are specifically thermodynamic i.e. that can be expressed as equivalent to doing work (and if not, then the question arises of how to establish an equivalence between the purposes for which a resource is actually valued, and a thermodynamic value in exergy terms). Gaudreau, Fraser and Murphy spell out clearly and in detail the basis for the problematic nature of exergy-based resource valuation here and here.[5], [7] Their summary findings are worth quoting directly:

Despite having many notable benefits, exergy is often misused by authors who tend to apply it as an intrinsic characteristic of an object (i.e., as a static thermodynamic variable)…Until the limitations are addressed, exergy should only be used for its original purpose as a decision making tool for engineering systems analysis.[5, see abstract];

The use of comprehensive reference environments may lead to incorrect recommendations and ultimately reduce its appeal for informing decision-making. Exergy may better inform decision-making by returning to process dependent reference states that model specific processes and situations for the purpose of engineering optimization.[7, see Abstract]; and

The initial exploration of comprehensive and universal exergy reference environments was beneficial because it provides an opportunity for deeper critical analysis of the opportunities and limitations of the exergy concept. At this point, however, the continued application of comprehensive reference environments for the purpose of characterizing resources and wastes, and even process optimization, risks reducing both the usefulness and credibility of exergy for informing decision-making. Now is the time to close the door on such applications, unless a complete reformulation of the concept is undertaken so as to avoid the limitations discussed above, while recognizing that such a reformulation may not even be possible. While many of the insights developed above are probably inherently recognized by many exergy practitioners (e.g., [65]), these problems have not been sufficiently nor formally recognized in the exergy literature. By recognizing and working within the constraints of exergy, the authors believe that exergy may still inform decision-making for progress towards sustainability. To do so, however, requires a deeper discussion of what insights can be obtained from thermodynamic analyses and what tradeoffs occur when the frame of reference becomes thermodynamic.[7, pp.2209-10]

As the conclusions from Gaudreau et al. quoted above state, these findings apply not only to resource valuation, but also to the quantification of environmental impacts from wastes. The reasons for this include, in addition to the problems with treating exergy as an intrinsic property of materials, even more fundamental issues. While the value of energy resources can be usefully considered in at least a loose conceptual sense in exergy terms—i.e. the value in which we’re interested, the capacity to do work, is indeed the same value that is measured by exergy analysis—only a small subset of the possible environmental impacts of wastes are measurable in such terms. There’s no useful sense in which we can draw a general equivalence between the exergy associated with a waste stream as it crosses the boundary between a thermodynamic system and its environment, and the impacts that the waste stream might have on that environment. Sciubba and Wall, in their review of the history of the exergy concept covering more than 2600 sources, could not be clearer on this (while also highlighting, in support of Gaudreau et al.’s findings, where exergy analysis is beneficial for addressing sustainability-related questions):

Exergy per se is NOT a measure of environmental impact, but in essence at the end of the life cycle of any device, plant and product, the exergy “balance” of the extraction-transformation-production-distribution-use-disposal cycle shows how many primary exergy resources have been actually used up (consumed), and there are already some studies that address the issue of designing “more exergy conscious” production cycles to attain a higher degree of sustainability. [3, pp.24-5]

I won’t push these arguments any further here. Clearly I’ve adopted a strong stance on this, and one that is rather at variance with the many researchers cited by the authors above who, despite these problems and limitations, continue to pursue work in this area. Still, I’m equally strongly in favour of using exergy analysis for sustainability-related assessment in the domains where it is well-established, rigorous and uncontroversial—this just addresses a more limited set of questions than some proponents might aim for.

This brings to a close the detailed exploration of exergy, or availability—the foundations that we’ll need for moving forward with the inquiry should now be pretty well established. In the next post (likely, as with this one in relation to the last, some way off at this stage) I’ll extend the systemic view of efficiency to take in a subject fundamental for the inquiry: Energy Return on Investment or EROI. Here again, the issue of conceptual tools as good servants but poor masters will be open for consideration. Later on, we’ll see how today’s post on exergy and the next on EROI form important parts of a more general view on the availability of energy—and why it is that, despite their vast magnitude, only a very small fraction of the energy resources to which we theoretically have access can be harnessed to do what we’d like them to do.

Notes

Note 1 To get a sense of how much temperature variation for a thermodynamic system’s environment can affect maximum theoretical work output, we can consider the Carnot efficiency—the theoretical maximum efficiency for any heat engine operating between a given set of high (heat input) and low (heat rejection, effectively that of the environment into which waste heat is discharged) temperatures. Take for instance a heat input temperature of 400^oC (673K)—roughly typical of the maximum steam temperature for a power generation process working on the steam Rankine cycle—and heat rejection temperatures of 0^oC (273K) and 40^oC (313K). (I’m using 0^oC here as the minimum because any lower, and the working fluid—water—could potentially freeze! Obviously, this would present some practical problems—the appropriate temperatures to use here don’t simply follow from ambient air temperatures). For the lower heat sink temperature, the Carnot efficiency is approximately 60 percent; and for the higher temperature, approximately 53.5 percent. For every 100 watts of heat input, theoretical maximum work output is 6.5 watts higher at 0^oC than at 40^oC.

References

[1] Gibbs, J.W. (1948), Collected Works, Vol. 1, p. 40, Yale University Press.

[2] Keenan, Joseph H. (1941), Thermodynamics, ch. XVII, pp. 289-313, John Wiley & Sons, New York.

[3] Sciubba, Enrico and Wall, Göran (2007), “A brief commented history of exergy from the beginnings to 2004”, Int. J. of Thermodynamics, Vol. 10, No. 1, pp. 1-26; viewed 14 May 2013 at http://www.ehakem.com/index.php/IJoT/article/viewFile/184/170&ei=vyatUImLIoiy0QX9jYH4Ag&usg=AFQjCNEM.

[4] Rant, Zoran (1956), “Exergie, ein neues Wort fur “Technische Arbeitsfahigkeit” (Exergy, a new word for “technical available work”)”, Forschung auf dem Gebiete des Ingenieurwesens, Vol. 22, pp. 36–37.

[5] Gaudreau, K., Fraser, R. & Murphy, S. (2009), “The Tenuous Use of Exergy as a Measure of Resource Value or Waste Impact”, Sustainability, Vol. 1 No. 4, pp. 1444-1463.

[6] Koroneos, C. J., Nanaki, E. A. & Xydis, G. A. (2012), “Sustainability Indicators for the Use of Resources—The Exergy Approach”, Sustainability, Vol. 4 No. 8, pp. 1867-1878.

[7] Gaudreau, K., Fraser, R. A. & Murphy, S. (2012), “The Characteristics of the Exergy Reference Environment and Its Implications for Sustainability-Based Decision-Making”, Energies, Vol. 5 No. 7, pp. 2197-2213.

[8] Corning, P. & J., K. S. (1998), “Thermodynamics, information and life revisited, part I: to be or entropy”, Systems Research and Behavioral Science, Vol. 15 No., pp. 273-295.