12. Amnesia amongst biologists: forgetting the origins of energy

Our planimeter has allowed us to connect differences in distances to areas. This is significant. It readies us for Newton who proffered and used his system of vectors and calculus twenty-six years after Boyle’s extremely influential The Sceptical Chymist, had been published, and four years before Boyle’s death. This important work extended Boyle’s ideas into what we now call chemistry and biochemistry.

Although Newton shared many of Boyle’s ideas, he has nevertheless often been cast as the party responsible for a separation. After him came a big shift in natural philosophy away from biology. He seemed to usher a self-consistent, systematic and thorough analytical mechanical structure into existence. His gravitational system also worked via the long-range forces that the planets exerted on each other. They were thought of as very different in kind.

But as witness Newton’s lifelong interest in alchemy, he is somewhat wrongly charged for he was nevertheless greatly interested in terrestrial events, and in the manner of Boyle. Having successfully unified celestial and terrestrial dynamics he sought to extend his accomplishment. On May 8, 1686, in the preface to his Principia, he wrote:

I wish we could derive the rest of the phænomena of nature by the same kind of reasoning from mechanical principles; for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other; which forces being unknown, philosophers have hitherto attempted the search of nature in vain; but I hope the principles here laid down will afford some light either to this or some truer method of philosophy (Newton, 1686).

In the section entitled “Queries” in his Optiks, he gave the strongest of his declarations that, in his opinion, all physical and chemical phenomena could be explained through an analogy with gravity. Terrestrial events, such as heat and light, would most probably work through short-range forces, but similar to gravity, arising from the interactions between the kinds of minuscule corpuscles Boyle had conjectured.

Have not the small particles of bodies certain powers, virtues, or force, by which they act at a distance, not only upon the rays of light for reflecting, refracting, and inflecting them, but also upon one another for producing a great part of the phenomena of nature? ... We must learn from the phenomena of nature what bodies attract one another, and what are the laws and properties of attraction, before we enquire the cause which the attraction is performed (Newton, 1730, Query 31, Book III).

One of the most important features of Newton’s system is its equating of potential and kinetic energies. However, this clear idea for a potential, in science, came from Jopseph-Louis Lagrange who tried to solve Newton’s three body problem (Bynum et al, 1983, p. 335). He devised the potential function to describe planetary behaviour. When he studied a given point in space, he sought a description for the gravitational force an infinitesimally small test body would experience at that given point. He observed that he could determine this by subtracting what later became George Green of the Green theorem’s “potential energy” from the kinetic energy that it would gradually acquire when it left that point and was subjected to the force inherent in the field (Green, 1828).

Thanks to Lagrange, potential energy, of whatever kind, is the stored capacity to do work due to an object’s position with respect to some reference. As with gravitational attraction, that reference is the place or condition to which the object will be transported on account of the energy it stores. Potential energy refers to the work or energy a body will undertake because of some other body, and or because of where it is when compared to that other body. If biology and ecology truly wish to emulate the accuracy and power of Newtonian or classical physics, then it is surely essential to find some kind of analogue for potential energy.

The eighteenth-century Scottish scientist Joseph Black took the first big step towards the discovery of a nonmechanical or non-dynamical version of Newton’s potential energy. A precursor to Lavoisier, Black also subscribed to the Boyle-Newton doctrine (Wilson, 2009; Donovan, 1976). One of his most notable contributions was based on his understanding of Newton’s third law. When a first body acts upon a second, then that second body has a reaction to the first. Black applied this Newtonian physics idea that if a first agent acts upon a second, that second agent will exhibit a reaction to that action to chemistry. This was his concept of a chemical reaction. The resulting chemical change is the “reaction” of the original substances to each other. As we shall see, this means that the reagents have a measurable potential energy with respect to the products.

Black also believed that heat was an important factor in determining the chemical affinities, or differential behaviours, of substances. His careful experimental studies played a major role in the development of chemistry as a modern quantitative science. He also noted that biology is impossible without the absorption and emission of heat energy in such chemical reactions. He was the first to think of directing his own breath at a sample of lime water, calcium carbonate, to properly quantify the effects of the ensuing gaseous reaction. It was the beginning of the journey to the modern doctrine that biological organisms survive by engaging in the systematic exchange of gases we know as respiration:

For I found, that by blowing through a pipe into lime-water, or a solution of caustic alkali, the lime was precipitated, and the alkali was rendered mild (Black, 1757).

Black also noted, in his investigations, that biology is impossible without the absorption and emission of heat energy, and he was the first to declare—although he was not the one to definitely prove—that respiration is a form of combustion accounting for animal heat:

Respiration is a type of combustion, and combustion is the source of heat in animals. (Black, 1803).

He also presciently noted that the amount of animal heat produced depended on the intensity of respiration:

the warmer animals are, the more perfect and constant is their respiration, and the more quickly do they infect the air with a malignant nature; may we not then suspect that animal heat and that alteration of the air arise from the same cause? (Rutherford, 1782).

He was again the first to carefully measure the masses involved in chemical reactions, and thus to distinguish between the quantity of heat in a body, and its measure of intensity, or temperature. He even went on to prove that a cyclical series of chemical reactions—which he determined was required for biology—is possible; that a gas is an independent chemical substance; that gases can react with solids; that heat tends towards an equilibrium; and that heat and temperature are distinct. All these, as developed by his successors, were necessary foundations for thermodynamics and the important Carnot cycle.

Black applied Gottfried Leibniz’s doctrine of the conservation of momentum to heat, and studied the changes in substances as heat was transferred from one to another (Ulanowicz, 1997, p. 21). Based on this idea, in 1792, he conducted an experiment in which he placed some ice-cold water into two pails, immersing them in an ice bath. He placed a drop of alcohol in one to prevent it from freezing, but let the other freeze over. He then placed them in front of the same open fire. The frozen pail took ten hours to melt, while the other rose to 140°F (78°C). (Black worked entirely in degrees Fahrenheit). Since, or so he concluded, the pails must have been absorbing heat at the same rate, then the heat absorbed by the frozen pail in ten hours was equal to the heat needed to raise the same quantity of water by 140 °F (78 °C) (Fenby, 1987, pp. 91–100).

Black’s discovery was significant. It posed a serious question which had to be answered. He had found a way to measure chemical configuration energy, a concept vital to biology. One pail changed its temperature under the impress of heat, while the other—as we now know—changed only its molecular configuration. Since the heat energy the ice absorbed was clearly “hidden” from his thermometer, Black called it a latent form of heat. We now call it the latent heat of fusion, and also know it as phase change enthalpy. It is a change in the Gibbs energy, which is a measure of chemical potential.

It is now important to remember that a difference in temperatures is also a distance. Black had realized that the heat absorbed by his first pail, per unit of its mass, could be measured as the second pail’s rise in temperature over that same time interval, and also per unit mass. Since this latter rise in temperature is observable to the senses, it is known as sensible enthalpy. Thus Black had observed that these seemingly different sensible and phase change enthalpies had the same magnitudes, and that he could accurately measure the one with the other. This presaged—again emanating from a biological discovery—the first law of thermodynamics, which declares the equivalency of all energy.

In another experiment, Black procured a small block of ice of known mass and placed it in some hot water, again of known mass, held at 190°F. When the ice had melted, the mixture had fallen to 53°F. He now knew the initial and the final temperatures—which is a distance—as well as the weights of the ice, of the glass, and of the water. He calculated that the ice-water mix was equivalent to a larger sample of water that had instead fallen to 143°F. The average of his two methods was now 141.5°F, the value he proposed for ice’s latent heat of fusion. In other words, he drew a conclusion about energy densities and transformations from a measure of distance.

Black’s methods may seem crude, but he was the pioneer. The key factor was his recognition of the interconnectivity between mass, its changes in configuration, and heat, and so between these different forms of energy, the one easily observed, the other not. He was within a most impressive 1.8% of today’s accepted values.

Black also soon determined that there was an equivalent latent heat of vapourization as water transformed into steam. He put a known quantity of water held at 50 °F (10 °C) in a flat-bottomed, tin-plated pan. It took four minutes to reach boiling point. He then noted that it took twenty minutes to boil away. Using the same reasoning as above, he concluded that water’s latent heat of vapourization was 810 °F (432 °C).

We can now recognize Black’s discovery of potential energy. We conduct a thought experiment based on Black’s experiments and his ground-breaking recognition of differences in chemical configuration —the beginnings in the understanding of chemical potential that biological organisms exploit. It is again about distances and their relationships.

Let there be two samples of water. One is Whypothetical. It never changes in its phase or chemical configuration, and always responds to sensible enthalpy. Our second, Wreal, is currently frozen as ice. It will respond to all incoming heat energy by expressing any relevant latent heats of fusion and vapourization. So as we now input heat, Whypothetical will keep its chemical configuration invariant throughout and only rise in temperature, while Wreal will additionally undertake any and all anticipated and expected changes in phase, which are changes in chemical configuration.

We now combine two of Black’s experiments. We have a heat reservoir containing precisely A joules of energy. It is exactly the amount required to carry Wreal through its various temperature transitions—a net distance—and its phase changes. When our thought experiment is concluded, the reservoir will be empty and there will be zero further potential energy available: A = 0. Taking the results of Black’s two experiments, then the potential final temperature, F, to which both our bodies of water have the potential to rise with this heat in our reservoir is 1,162 °F (628 °C). But we of course know that Wreal will not reach that temperature. Its final temperature, also a distance, will in fact simply be the final measured boiling point of water, M. But if there is a difference between F and M, then it can only be because Wreal has undergone some phase transitions which have diverted that energy from the sensible to the phase change enthalpies.

We now remove some heat from our reservoir and direct it at our two samples. Our potential energy source, A, has therefore decreased and has less energy available. Since it has tended to zero then → 0.

The heat we have just removed from our reservoir is just enough to permit both our bodies of water to raise their temperatures, again a distance, by 1 °C. Since Whypothetical always responds with sensible enthalpy, it rises by exactly this 1 °C. Therefore, the final temperature, F, to which it can still rise, under additional future injections of heat energy, remains the same. Its chemical configuration does not change. That is to say, its distance to be travelled remains invariant. However, since Wreal is currently frozen, it cannot respond with sensible enthalpy. Instead of rising in temperature, it must first change its chemical configuration and melt. Its potential distance to be travelled must in this case change, and the quantity of distance lost is the measure of the change it undergoes.

Since the heat in our reservoir is limited, then the potential final temperature to which Wreal can now rise, under additional injections from our reservoir, has changed by 1 °C to ( - 1) °C. It therefore has less potential available for sensible enthalpy responses, which are increases in temperature and distances, because it has again diverted some into the phase change variety. And since the potential final temperature to which Wreal could now rise has fallen, it has tended one degree closer to its observed final and measured temperature. It can only now travel a shorter net distance, and → M. This difference between F and M tells us exactly what has happened to Wreal. It has undergone a phase transformation or change in energy density.

If we again remove that same amount of heat from our reservoir and inject it into our two samples, then Whypothetical will rise by a further 1 °C while Wreal melts yet further. Our heat reservoir has again tended to completion, i.e. A → 0, while the potential distance of temperature to which Wreal can now rise has declined yet further by one degree, because it has again changed its state and augmented its configuration energy. So we again have FM.

For every further injection of heat energy that causes a phase change in Wreal, our Whypothetical will rise ever closer to the initial hypothesized temperature F, by 1 °C … but we will have to reduce the potential final temperature to which Wreal—i.e. the distance which it can travel—could yet rise by 1 °C, and so closer to M, to compensate for its change in phase. If there were no variations in its chemical configuration or energy density, then Wreal would always behave exactly as Whypothetical. It would travel the same distance, and it would reach the same final temperature. But since it changes phase, it does not. Therefore, for every exertion of Wreal’s phase change enthalpy, the projected final potential temperature, F, remaining available to it under further injections of heat, will ever more steadily approach its actual and final measured boiling temperature, and such that FM. The final difference in distance between F and M will quantify all variations in configuration that Wreal has undergone when compared to F and Whypothetical, which now act as standards. Our planimeter can handle all such situations

As Black demonstrated, this method is completely general. It embraces all possible changes in phase or configuration, and all temperature transitions between them, no matter how many or how diverse. There exists a Whypothetical that is a potential and a match for them all. We can always and in principle use Whypothetical to match any real final temperature, M, no matter how many or how complex the phase changes and temperature transitions Wreal goes through. We can always calculate both the potential energy, A, for any and all such real samples, and then also an initial hypothetical temperature, F, that any and all such samples would rise to if they ignored all such phase changes or changes in configuration. They may be exhibitions of different kinds of enthalphies or energy behaviours, but by the first law of thermodynamics, all energy is equivalent. At the completion of any such experiment, our potential heat source will be exhausted and also such that, no matter what the changes and variations the real sample has undergone, both = 0 and M, with the distance that F has travelled from its original value to M being a measure of the change in energy density. The measure of one tells us how much energy has been devoted to the other.

Not only is this method completely general through being applicable to heat, but by the first law of thermodynamics it is all the more general through being applicable to all forms of energy—including the biological. Black’s chemical configuration variations in fact represent all variations in energy density. Wherever there are two or more states—again including the biological—differing only in their chemical configuration or energy densities, then by this first law it will always be possible to express all the states in terms of one, and through some measurable property—a distance—exhibited by them all, and which is then taken as invariant in a selected one. That selected one is then the standard of measure. Variations in energy are then expressed through differences, amongst the others, in that measurable property. This fact regarding potentials and actualities and measurements of energy and energy density—which we can again think of as distances and areas—will become significant shortly.