In last week’s post I commenced a brief and highly selective look at the history of the energy concept. The purpose of this historical approach to our inquiry is to get some sense of how the pioneering investigators might have made sense of their experience of the physical world, unaided—and hence also, in a sense, unconstrained—by the conceptual tools that we take for granted today. This in turn might help us to get a better sense of what the energy concept is all about in experiential terms. The aim of all of this is to ensure that, in thinking about societal energy challenges and dilemmas, we hold the conceptual tools, rather than the conceptual tools holding us.
We started out in Part 1 by considering some of the early forerunners of the modern energy concept through the work of Galileo, Descartes and Leibniz, all important pioneers in the branch of physics known as mechanics. While the contributions of these investigators all preceded the arrival of the earliest heat engines—the general class of machines that enabled the rise of industrial society, and that continue to provide the overwhelming majority of electricity and transport today on a global scale—they had little direct influence on the rise of the mechanised world. For most practical intents and purposes, we can consider the historical precedents of the modern energy concept in terms of two largely independent paths: the physicists and mathematicians travelled by one route; on the other, we find the engineers. These paths would eventually undergo a significant convergence, but at the end of the seventeenth century, the two groups typically had quite distinct interests. While we might say that the physicists tended to focus on describing and explaining physical phenomena, the engineers were interested in harnessing physical phenomena for practical human purposes. Nonetheless, there were still important instances of crossover between the groups. The French physicist and mathematician Guillaume Amontons (1663-1705) was an important figure in this respect. Not only did he propose a conceptual design for a novel heat engine, in work published in 1699 he attempted to quantify its useful effect in terms of the labour of “men and horses”, still at that time the dominant prime movers for most areas of economic activity. In doing so, he effectively pre-empted the concept of work.[1] Motivated by the engineers’ need for a means of quantitatively comparing performance amongst different types of machines, the work concept as we know it today emerged during the early years of the eighteenth century.[2]
Heat engines—or as they were typically known during the historical period of their emergence, fire engines (later, steam engines)—had been envisaged, and even demonstrated, well prior to their practical arrival in forms capable of shaping the economic landscape. In fact, the earliest known example is Hero of Alexandria’s aeolipile, c. 60 AD. Until the early eighteenth century though, these were of little more than novelty value, so limited was their performance compared with established means of carrying out work. This was about to change. The critical turning point in the steam engine’s evolution can be traced to 1712, in Dudley, England. In that year, Thomas Newcomen (1663-1729) built the first engine to carry out a practical task—pumping water from a coal mine. At 3.75 kilowatts [3] (we’ll look in detail at what this means in a later post), the output of Newcomen’s engine was equivalent to the labour of around forty people working continuously (and far more than this number, allowing for the proportion of each day for which any individual could actually maintain such a work rate!). Even with an estimated maximum efficiency (another subject for a later post) of only 0.7 percent [4], the machine improved mine productivity sufficiently to establish its value. Along with subsequent performance improvements, this ensured its rapid spread to coal mines elsewhere, and eventually to mines for other resources. The great significance of the engine lay in the contribution that increased mine productivity made to the economic viability of coal as a fuel—a new technology, enabled by a naturally-occurring fuel resource, enabled in turn the growth in exploitation of that resource. We see here the basic character of the positive feedback process that I previously described in relation to the planetary-scale systems view in Thinking with systems—Part 2.
The Newcomen engine and its incremental variants remained state-of-the-art for a further half-century. Throughout this period, engineering practice ran well ahead of the capacity to provide an overarching mathematical and hence quantitative account of just what these machines were doing. As Coopersmith puts it “The success of the ‘fire-engine’ could not be questioned; the physics would just have to catch up”.[5] In fact, Newcomen’s fire engine was constructed at Dudley five years before the first use of the term ‘energy’ in physics, by Johann Bernoulli (1667-1748). Even then, the narrow context in which he used the term would have provided no practical guidance to the engineers, had they been aware of it.
Early signs of potential energy
Around this time, though, physics was on the cusp of a development of tremendous importance—one that would be both essential for and instrumental in advancing the general view of energy yet to come. Johann Bernoulli played an important role here also; the contribution of his son, Daniel (1700-1782), was more significant again. Last week, we saw how Leibniz had introduced the concept of vis viva, the forerunner concept to kinetic energy. But we know today that a complete account of a physical system’s behaviour also requires a complementary quantity, the potential energy: where would this enter the picture? As it turns out, Leibniz had also proposed a related quantity, vis mortua, or ‘dead force’, as the source of a general ‘propensity to motion’.[6] In 1728, Johann Bernoulli advanced this view significantly by recognising vis mortua as stored ‘live force’, and associated this with a range of physical phenomena including compression of springs—this was an important step towards identifying an equivalence between ‘dead force’ and ‘live force’.[7] It was Daniel Bernoulli who, in 1738, made this connection explicit, and who first used the term ‘potential live force’ in relation to the complement to ‘actual live force’ that he recognised as necessary for conservation of ‘activity’, or of ‘cause and effect’.[8] It’s particularly noteworthy that he specifically connected this new conceptual view with the practical appraisal of machine performance; he even went as far as to assess the ‘stored live force’—the work potential—of quantities of coal and gunpowder.[9]
Some views on heat
As we know from our earlier discussions, the relationship between heat and mechanical work lies at the heart of the modern energy view. The engineers by this time had clearly run well ahead in terms of connecting—practically, not conceptually—these physical phenomena. In terms of the physicists’ side of the story, we’ve focused to date on the early developments in mechanics, the study of the macroscopic-scale motion of matter. This has carried us well along the way to a full account of the aspect of the energy concept to which mechanical work relates. We’ve not yet looked at what the physicists were making of the other phenomenal aspect of the energy concept, heat. This is a timely place to take up that thread in the story, given the significance of Daniel Bernoulli’s role. Before we look at that, however, we’ll take a step back to the seventeenth century, and the work of Robert Boyle (1627-1691). With his views on the physical basis of heat published in 1665, Boyle was certainly not the first to recognise heat as due to the motion of a body’s constituent parts. Even so, he was well ahead of his time in appreciating that the distinction between the phenomenon of heat and that of the bulk motion of material bodies through space was a matter of scale, rather than the underlying natures of the substances involved.[10] For Boyle, heat related to the internal motion of a material body, the motion of its constituent parts. He understood this motion to involve high speeds and uncoordinated directions, an account he arrived at by inference, from observing the behaviour of fire, and water droplets falling on a hot surface.[11]
From the point of view of our inquiry, the particular significance of Daniel Bernoulli’s contribution to the mechanical—or motional—theory of heat lay in his application of this view to a kinetic theory of gases. In his 1738 book Hydrodynamica, Daniel Bernoulli considers a gas as a collection of minute particles moving with very high speed. Perhaps most importantly though, he considers this kinetic behaviour in terms of a volume of gas contained in a cylinder of variable volume, i.e. enclosed at one end by a piston—once again, this connects his work in the field we now know as physics, with the work of the engineers and their heat engines.[12] In Daniel Bernoulli’s account, pressure is due to the particles colliding with the cylinder walls and underside of the piston; this pressure increases on heating the gas, due to the associated increase in the speed of the gas’s particles, requiring the application of an increased weight to restrain the piston. In this respect, his characterisation of a gas is for all intents and purposes the contemporary view. Even so, a century elapsed before the prevailing thinking caught up.
A new measure of motion: the action
So far, we’ve seen the emergence of many of the critical precedents to our energy law 1, and some early precursors to the territory dealt with in energy law 2. The next significant development to unfold relates to our energy law 3: the Principle of Least Action was introduced in 1744 by Pierre-Louis Moreau de Maupertuis (1698-1759), and also proposed a year before this by the mathematician Leonard Euler (1707-1783), who nonetheless, being less sure of its basis, recognised Maupertuis’ priority. This principle reflected Maupertuis’ reasoned view that “nature is economical with her resources and always acts in the most efficient way possible”.[13] On the basis of this, Maupertuis proposed a new quantity, the ‘action’, that he defined as mvs, the product of a particle’s mass, speed and distance travelled; his principle required that the path taken by the particle correspond with the minimum value for the action. These insights were taken forward by Joseph-Louis Lagrange (1736-1813) as an essential foundation for his Analytical Mechanics, published in 1788. This work—groundbreaking in its own time, and central to physics today, as discussed in Thinking in systems—Part 3—provided both an account of and a way of analysing physical systems in what Lagrange intended to be the most general terms possible. Specifically, and of central importance to the story unfolding here, he developed a way of looking at the physical behaviour of a system—the system-relative motion of its parts—in terms of what subsequently became known as the kinetic and potential energy. In Lagrange’s mechanics, the system under investigation is described in terms of the kinetic and potential energy of each of its components, and this provides a basis for determining what happens to the system through time, in a way that is general for all systems regardless of their particular situation-specific physical composition and configuration. But what motivated development of this general approach to ‘what happens through time’? Coopersmith’s account of this is particularly significant for our own inquiry: she frames this in terms of a quest to “identify the truly invariant features of the mechanical landscape”, for the physical situation under investigation.[14] The particular feature that turns out to be invariant for a given situation defined in mechanical terms—in terms of masses in motion—is the minimum value of the action.
It may be worth pausing here for a moment to think about what this entails in terms of the distinctions introduced two weeks ago between events ‘in-and-of-themselves’, our mental experience of those events, and our conceptual accounts of our experience. What we’ve effectively learned above is that for any physical event that we care to bound in space and time—think for instance of our example from several weeks back of a water bottle falling vertically from rest through some specified distance—there is a single quantity that characterises the event not just at any particular time, but for the full duration. In other words, we can reduce everything that we regard as significant about that event, for its entire duration, to a single quantitative measure. Moreover, because we know that for the actual way the event occurs—how it plays out between initial and final states—this quantity must be the minimum of all possible values, a means is available to us for developing a complete description of the event through space and time. That is, we can fold everything about that event into a single number, discarding all other particular details. And, most remarkably, provided that a) the total energy over the course of the event is conserved, and b) that we can describe the kinetic and potential energy for an appropriately defined system with which the event is related, we can actually recover a detailed description of the event in terms of a set of mathematical equations describing the system’s motion. To appreciate the significance of this, we can compare the action, as a description of a physical system through time, with the total energy. The total energy is the sum of the kinetic and potential energy; for an isolated system, the total energy is conserved i.e. it is constant. For the actual path that the system follows, the total energy of the system for the duration of the event in which we’re interested is described by a horizontal line. For the same actual path, the action on the other hand is described by a single value and hence a point, rather than a line. Considering this in a slightly different way, for a given system, there is a set of possible events that can occur, depending on the system’s degrees of freedom. To describe each event in the set in terms of the associated total energy, a family of curves is required. Describing each event in the set in terms of the action, on the other hand, requires a single curve. Every event in the set corresponds with a point on this curve.
Any conceptual description of our perceptual experience involves some level of abstraction—we reduce all of the possible detail of the perceived situation to which our experience relates down to some subset that we regard as most important and hence most worthy of our attention. In doing so, we divert our attention away from the particular aspects and nuances of the situation that mark it as unique, relieving ourselves of the cognitive burden of holding in mind all of that nuance. In describing an event in terms of the action associated with it, we discard more of the details about the event than when we describe that same event in terms of the energy associated with it. In other words, the action involves a higher level of abstraction from the particular details of the event than does the energy. In this respect, the action can be regarded as a more abstract and—hence a more fundamental—measure for a mechanical system than the total energy. With reference to the earlier efforts of Descartes and Leibniz to define a ‘quantity of motion’, we can now say that for an event—i.e. for a given set of changes in a physical system’s configuration taking place over some period of time—the most fundamental measure for this is not the momentum, nor the kinetic energy, nor even the total energy, but the action. The systems view is central here: whereas the energy relates to the ‘quantity of motion’ at each point in time during an event, and hence corresponds with the system state, the action relates to the ‘quantity of motion’ for the entire unfolding of an event through time, and therefore takes into account all system states between the event’s observer-defined start and finish. In other words, the action describes—mathematically, in the simplest possible terms—‘what happens’ during a physical change process. Nonetheless, this description—the value calculated for the action—is still relative to the system that we define as relevant for the event in which we’re interested. The action is not a pre-given ‘essential feature’ of the physical event itself—it is a conceptual construct created for our own very human communicative purposes.
James Watt’s engine: a prime mover for the Industrial Revolution
During the period in which these developments of such great significance to physics were unfolding, similarly momentous advances in engineering were also taking shape. It’s of particular note that these were in important respects a result of the scientific method at last being applied in a systematic way to industrial problems, including improvements in machine design.[15] The figure of greatest historical significance in this respect was perhaps James Watt (1736-1819). When Watt turned his attention to improving the performance of the steam engine in 1765, this technological arena was still dominated by Newcomen’s fire-engine—or at least, incrementally improved versions of the early design. There had been no expansion though in the application of these engines—they were still used almost exclusively for pumping water from mines. The technology was simply too inefficient in its use of fuel, and its mechanical output too crude in form, to garner significant interest in adapting it to other purposes. Watt’s first patent, issued in 1769, was for the addition of an external steam condenser to the fire-engine. This allowed the cylinder in which the reciprocating piston moved to be maintained continuously at close to the steam inlet temperature, while the condenser was maintained continuously at the low temperature required to condense the steam to water after it was discharge from the cylinder’s exhaust outlet. This allowed a much higher proportion of what we later came to recognise as the available thermal energy associated with the steam to be converted to mechanical work. When the new design was put into commercial production after 1775, this innovation increased the efficiency of Watt’s engine by a factor of four compared with other engines of the time that were based on Newcomen’s original design.[16] The efficiency gain and attendant increase in mechanical output resulted in the new design quickly being recognised as attractive for an expanded range of applications. Even so, the single-acting piston stroke (steam drove the piston in only one direction) resulted in a mechanical output that was still suited only to pumping water. Conversion to rotary motion was achieved by elevating water that was subsequently used to drive a water-wheel—Watt’s engine remained a steam-driven water pump. Watt did not stop at this though. Between 1781 and 1788, he patented four further innovations: the sun-and-planet transmission to convert the linear reciprocating movement of the piston to a rotary output; the double-acting cylinder, to drive the piston in both directions during its stroke; the parallel motion, to allow the connecting rod for the piston in the double-acting cylinder to remain parallel with the cylinder centreline throughout the piston’s stroke; and the governor, for automatically regulating an engine’s output speed via a form of mechanical feedback control. These developments revolutionised the steam engine, and enabled the industrial transformation of every area of manufacturing.
While they’re certainly of broader interest to our inquiry, these practical engineering developments don’t in their own right advance our understanding of the energy concept’s historical unfolding. Watt did, however, also make important contributions in this respect: he defined an engine’s efficiency, or duty, as the ratio between the work done—defined by established engineering convention as a weight lifted through a given height—and the quantity of fuel used; and he introduced the horsepower as a measure for the rate of doing work, defining this as 33,000 foot-pounds per minute.[17] In doing this, Watt not only brought conceptual rigour to the design and performance assessment of steam engines, but made an important contribution to establishing the conceptual connection between the phenomena of heat and work.
Converging paths in engineering and physics
Watt was one of the pioneers in bringing together practical engineering with the scientific method, but others played similarly significant roles in this area. In the context of this very selective overview, two others especially stand out in their use of engineering-related insights to advance understanding of the energy concept more generally: Lazare Carnot (1753-1823), and his son, Sadi Carnot (1796-1832). Lazare’s contribution centred on the analysis of machines in terms of the general principles of their operation. Taking the water wheel as his prototypical machine in this respect, he considered the micro-scale physical behaviour by which the input motion of the water was converted to the wheel’s motion—the machine’s work output—and proposed fundamental principles by which this conversion would be maximised. In this way, he introduced a new approach to thinking about the physical behaviour of bulk matter in terms of micro-scale constituent elements, a significant development both for scientists and for engineers. His 1783 publication relating to this established the relevance of the engineering concept of work—as the product of force and the distance over which it is applied—for physics.[18]
We’ve seen some very early indications of the conceptual territory summarised by energy law 2 in our discussion of motion theories of heat, specifically in the work of Robert Boyle and Daniel Bernoulli. With Sadi Carnot’s pioneering investigations into the relationship between the heat input and work output for heat engines, we now arrive at the explicit origins of that law for the first time. Sadi’s work follows from and can be considered as an important extension of that of his father, Lazare. While Lazare had investigated the general principles relating to the operation of machines for converting mechanical inputs to mechanical outputs, Sadi was interested in the extension of this approach to all machines, including those driven not by mechanical input associated with bulk fluid motion, but by heat. The eventual result of his work was the establishment of an expression for the maximum possible conversion of heat input to work output for an ideal heat engine. This is the maximum theoretical efficiency that cannot be exceeded by any heat engine for a given set of operating conditions. Today this is known as the Carnot efficiency, ηc, and is defined as follows:
In this expression, Thot is the temperature, in the absolute or Kelvin scale, at which the ideal engine’s heat input is delivered; Tcold is the absolute temperature at which heat is rejected to the engine’s environment. This heat rejection is necessary for the engine’s continuous operation. In order to provide this continuity, the working fluid that drives a mechanical actuator to deliver the work output must pass through a closed cycle of states, starting in some initial state and returning to this state before commencing another cycle. As the fluid passes through this cycle, its temperature initially increases as it passes through a heat input stage, approaching the hot temperature of the heat source; it then flows to the actuator, doing work on the output device, before flowing through a heat output stage in which its temperature decreases, approaching the temperature of the heat sink (the engine’s environment). At the end of this heat output stage, the fluid has returned to its initial state.
This isn’t the place to dwell further on the specifics—that can wait for a later stage in our inquiry. I will highlight three points here though:
1) Sadi Carnot’s insight represents a case of undisputed genius, foundational to the whole of thermodynamics, and hence of unsurpassed significance in relation to the industrial developments that support our modern way of life;
2) The Carnot efficiency relates to an ideal heat engine—as such it represents an absolute performance limit for heat engines. No real heat engine can achieve this efficiency, and in fact even the most efficient real engines fall well short of this for a wide range of practical reasons;
3) It is essential to keep in mind that this insight applies exclusively to the class of devices known as heat engines i.e. devices for converting heat input to work and heat output (a consequence of the heat rejection stage noted above—a feature of every heat engine, regardless of the specifics of its operation—is that a portion of the heat input must leave as heat; we know from energy law 1 that this ‘waste heat’ output is equal to the heat input minus the work output). The hot temperature is specifically the temperature of the heat source that is brought in contact with the working fluid.Note 1
The most pertinent aspect of Sadi Carnot’s work for the present stage of our inquiry is the finding that it is a temperature gradient that is the ‘driving force’ for a heat engine. Whereas in machines such as the water wheel studied by Lazare it was the conversion of the bulk motion of a fluid (flowing from a higher to a lower reservoir) to the motion of an impeller that provided the work output, in the case of the heat engine Sadi realised that it is heat ‘flowing’ between high and low temperature reservoirs that provides this ‘motive power’ output (his seminal paper, published in 1824, was titled Reflections on the motive power of heat). The relationship with energy law 3 will hopefully be apparent—we’re dealing here with a dispersal process, a process by which ‘motion’ spreads out via a gradient between higher and lower concentrations. We’re now homing in on the immediate significance of Sadi’s work here: he conducted his investigations at a time when the prevailing view was of heat as a special substance–or ‘subtle fluid’, known as caloric—rather than heat as the small-scale motion of a bulk material’s constituent parts. Despite the significant agreement between our contemporary kinetic or ‘motional’ understanding of heat and the earlier view held by the likes of Robert Boyle and Daniel Bernoulli, those views had not prevailed through the eighteenth and early nineteenth century. While there were supporters for both the motion and substance theories throughout this period, the substance theory held greater authority due to its explanatory power across a wide range of observed phenomena. In many cases, heat-related findings based on that theory were also entirely consistent with the motion theory. Consequently, when the substance theory was eventually abandoned altogether in the mid-nineteenth century, much of the earlier work on heat remained relevant. This was the case with Carnot’s work. Carnot initially assumed that the total quantity of heat must be conserved: total heat input must be equal to total heat output. As it transpired, his overall findings were correct, despite him being wrong in this respect.
Even so, as Coopersmith reports, between the preparation of the manuscript for Reflections on the motive power of heat, and his death in 1832, Carnot’s thinking underwent a comprehensive revision. Coopersmith summarises his eventual views, expressed in a collection of notes discovered after his death:
we can see that Carnot’s thoughts evolved away from the caloric theory and to the dynamical theory of heat. He came to realize that: heat cannot be material, it must be ‘a motion’; all motive power is ‘motion’ of one sort or another; and that interconversions are possible, but not the creation or destruction of ‘motion’.[19]
Change in motion: a general view emerging
The recurring emphasis on motion amongst the pioneering investigators whose insights we’ve consulted seems to corroborate pretty well the view outlined here at Beyond this Brief Anomaly regarding the energy concept’s status. Given this thoroughgoing relationship between motion and the energy concept, it doesn’t seem particularly controversial to point out that energy’s existence lies within our own interpretive and communicative structures, rather than in ‘physical things themselves’. In fact, Coopersmith’s summary above seems to suggest that it might not be at all unreasonable to draw a parallel between the shift in understanding that played out in the nineteenth century in relation to heat and the shift advocated here from viewing energy as an inherently existent entity, to viewing it as a conceptual construct for describing perceived invariant tendencies associated with physical systems.
But I’m perhaps getting a little ahead of the game here. Our story is not complete: the modern view of energy, in which a common conceptual construct provides a unified account of a world that, across all of its diverse material forms, is fundamentally dynamic, is—even with Sadi Carnot’s posthumous insights—yet to emerge. Next week, I’ll close out this series of posts with the final instalment focusing on the developments that ushered in what we might reasonably call the age of energy.
Notes
Note 1 The working fluid allows for a continuous temperature gradient between the hot source and the cold sink; Carnot’s analysis required that there be no discontinuities and this temperature was specifically related to a heat reservoir in direct thermal contact with the working fluid. I emphasise this particular point because I’m aware that some people, having heard about the Carnot efficiency, assume that it applies to all energy conversions involving a work output and a nominal set of hot source and cold sink temperatures, without reference to the specific nature of the thermal connection between that source and sink; for instance, I’ve seen it discussed in relation to evaluating the maximum possible efficiency of conversion for solar radiation to useful energy output, using the surface temperature of the sun as the basis for the hot temperature. Here’s an example of such use. The surface temperature of the sun is not the appropriate hot reservoir temperature in such an analysis—except in the case where the ideal heat engine is placed in direct contact with the surface of the sun itself! In fact, for a practical heat engine using solar energy as its heat source (a concentrated solar power tower, for example, such as those recently proposed to play a pivotal role in transition to a solar powered economy), the hot reservoir cannot possibly be at the same temperature as the surface of the sun, as the temperature differential between the sun’s surface and the hot reservoir would then be zero, and hence there could be no radiant heat transfer. The example that I link to above is a significant one—the author is highly credentialed and widely respected (I generally share this regard) within the broader community of inquiry to which Beyond this Brief Anomaly is intended to contribute. So errors such as this are not just restricted to non-specialists and lay people, perhaps underscoring the importance of Beyond this Brief Anomaly’s stated mission with respect to advancing general energy literacy.
Incidentally, it’s somewhat ironic that the error is made in an attempt to refute the thermodynamic arguments of a non-specialist, John Michael Greer at the Archdruid Report. Greer’s original argument about the prospects for solar-powered civilisation, based on the low energy concentration associated with solar radiation, is highly relevant to our own inquiry, and we’ll be taking this up in much closer detail as we proceed. The starting point for that will, contrary to Stuart Staniford’s rebuttal, take Greer’s principal concern as well founded and essentially on the right track—as we’ll see, energy concentration is an important and highly relevant basis for a high-level appraisal of the prospects for diverse energy sources. What I’m hoping we might add to that is some more comprehensive thinking about exactly why this is important, and perhaps the nature and extent of the limits involved.
Bibliography
Magie, William F. (1935). A source book in physics, McGraw-Hill Book Company, New York.
This is an anthology of excerpts from the original publications of physicists (as we now know them) from Galileo onwards; it includes work from many (though not all) of the pioneering investigators covered in this and the previous post. This has provided a convenient way of reviewing some of the original sources, particularly where these are not quoted directly in the principal secondary reference that I’ve drawn on, Coopersmith’s Energy: the subtle concept.
References
[1] Coopersmith, Jennifer (2010). Energy: the subtle concept, Oxford University Press, Oxford, pp. 60-61.
[3] Smil, Vaclav (1994), Energy in world history, Westview Press, Denver, p. 161.
[5] Coopersmith, Energy: the subtle concept, p. 77.
[15] Ashton, Thomas S. (1948). The Industrial Revolution, 1760-1830, Oxford University Press, Oxford.
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