27. Discovering the energy of natural selection

The issue, now, is how molecules behave when their interaction with the environment—i.e. across the system’s boundaries—is considered and so that they do work. Such were Mayer’s insights into the relevant issues, gained entirely through biology, that in 1842 he went so far as to calculate his first value for a universal constant of nature now called ‘the mechanical equivalent of heat’. He analysed the results of some experiments performed in France that all others had failed to explain: why the specific heats of gases held under constant pressure, CP, were always greater than for those held under constant volume, CV. Mayer, working from first principles, and with only phenomena in biology and physiology as his guide, insisted that he knew the reason.

Figure 26: Constant Volume: Non-Mechanical Chemical Energy
 Constant Volume: Non-Mechanical Chemical Energy

We imagine, as in Figure 26, a closed container of volume V initially containing ice. A boiler is underneath and we have a refrigeration unit available for later use. We can measure density and all other properties as the water responds to our various injections and removals of heat by changing in its phase. Since the volume is constant, the water is completely free to change its molecular configurations. Density will change consistently with the temperature, T, and with the amount of heat, Q, injected and removed. The water is free to adjust its overall pressure, P, within the given confines, and according to its state at each given temperature. It expands, contracts and transforms between ice, liquid water and steam as appropriate, all within the confines of its constant volume system. We can measure a distinctive rate of change, for every substance, of heat, Q, with respect to temperature, T, as the volume, V, is kept constant. It is (Q/T)V = CV.

Figure 27: Constant Pressure: Mechanical Chemical Energy

The constant pressure case of Figure 27 is importantly different. The relevance is that biological systems must use energy. They must manufacture chemical bonds to take in molecules from, or release them back into, the environment in growth, reproduction, and eventual dissipation.

Murray correctly points to the origins of the modern analysis of this second constant pressure situation:

Bernoulli later deduced Boyle’s Law from Newton’s Second Law and the further assuumption that gases were particulate in nature (Murray, 2001).

But although Murray is correct in pointing out that modern analysis of this case is now based upon the molecular theory of gases developed by the Dutch-Swiss mathematician Daniel Bernoulli, as now seems standard throughout the biological and ecological sciences, he does not properly note the significance. We shall have to return to the significance later, but it is critical.

We for now accept that Boyle was indeed the first to propose gases as particulate, and that Bernoulli was the first to properly understood—and calculate—that air pressure is a product of molecular momentum:

Consider a cylindrical vessel … set vertically, and a movable piston … in it, on which is placed a weight P; let the cavity … contain very minute corpuscles, which are driven hither and thither with a very rapid motion; so that these corpuscles, when they strike against the piston … and sustain it by their repeated impacts, form an elastic fluid which will expand of itself if the weight P is removed or diminished, which will be condensed if the weight is increased …. Such therefore is the fluid which we shall substitute for air. Its properties agree with those which we have already assumed for elastic fluids, and by them we shall explain other properties which have been found for air and shall point out others which have not yet been sufficiently considered. We shall consider the corpuscles as practically infinite in number … (Bernoulli, 1738, p. 774).

In this second constant pressure, CP, situation, instead of leaving the water free to change its state, we place a piston upon the system. It is now, therefore, confined. In the ice and liquid phases, the piston rests on the surface and the volume, V, is at a minimum. But when the water becomes steam it seeks to increase its volume. Unfortunately, the piston’s weight is a constant impediment. Expansion imposes a mechanical overhead. Therefore, said Mayer, the gas must take in extra heat energy to allow for pushing the piston up against the atmosphere, and moving its molecules onto and away from the system’s boundaries. Bernoulli’s model even allows that extra energy of working against the environment to be computed. The total depends on the forces and the distances those molecules must travel to effect the work they must now do, for they are all subject to Newton’s laws of motion. For every substance, there is a different but equally distinctive rate of change of heat taken on, Q, with respect to each change in temperature, T, as the pressure, P, is kept constant and as it moves against a weight. This latter rate of change is expressed through the formalism (Q/T)P = CP.

With his new energy concept Mayer then related these two expressions. Every system will have one thermal capacity covering what happens to it when it does some associated mechanical work and lifts a weight, but without any necessary and associated changes in volume or configuration. This is simply to work against the environment and to move molecules in and out. But every system will also have another capacity when it simply changes configuration, and also possibly even expands, by changing configuration, but without any overhead in a change in weight, and so without moving molecules across or against the system’s boundaries. Although heat is consistently emitted or absorbed in both situations, a mechanical aspect can always be contrasted with a nonmechanical one for every system. It is always possible to separately measure both these kinds of heat and work.

This concept holds generally. In Mayer’s view, this propensity holds even for biological organisms, which will also have one energy signature when they do a specified amount of work in the environment; and another when they only change configurations internally and do not work against the environment. Without recognizing this distinction between the intrinsic and the extrinsic, any hopes for a truly scientific biology are doomed. As we shall again clarify shortly, biologists and ecologists have consistently refused to acknowledge this distinction.

Mayer used the results of the French experiments to calculate both the mechanical equivalence of heat and the universal gas constant, R, that explains the behaviour of all gases. “Mayer’s relation” is: CP - CV = R. It can also be given by CP - CV = R/J where the specific heats are then expressed by the mole, and J is the mechanical equivalent of heat. Mayer—as a biologist and physiologist—was therefore the first to publish a quantitative value relating the calorie, as a unit of heat, to what we now call the joule, a unit of energy named in honour of Joule. Mayer, however, had clear precedence in noting that J = W/Q where W is the work done and Q is the heat provided, with J then being a constant of nature. The values are completely independent of the methods by which either work is done or heat is produced. One calorie is the amount of heat—or other form of energy—needed to raise one gram of water by a temperature of one degree Celsius; whereas one joule is the amount of work or energy required to accelerate a mass of one kilogram so that its velocity increments at the rate of one metre per second per second. The two are equivalent. Since a force has to be exerted to provide that acceleration or increment of velocity, then work is being done to produce that acceleration, and that—by the first law of thermodynamics he went on to propose—the work could equally well heat the water. A joule is the unit measure of work done, and therefore the unit quantity of energy expended, in so exerting a force of one newton.

Mayer saw clearly that one kind of activity or endeavour is being converted to the other … which, he insisted, is exactly what biological organisms are also, and always, doing. This is the principle of the interconvertibility of energy, without which biology is impossible. A calorie, as heat energy, is capable of achieving this precise effect, and one calorie is equivalent to 4.184 joules. Mayer’s paper On the Quantitative and Qualitative Determination of Forces gave his first value for this mechanical equivalence of heat. In his Remarks on the Forces of Inorganic Nature he published his view that oxidation was the primary energy source of all biological organisms. He was by now convinced (a) that both organic and inorganic entities obeyed the same rules, and (b) that energy could not be created from nothing. His view of it embraced the universe and became enshrined as the first law of thermodynamics. This is a basic of science.

Unfortunately for Mayer, his overall results were ignored by all and sundry … and due to a nationalistic fervour engendered in the United Kingdom in support of Joule, Mayer’s prior discovery of, and contributions to, the energy doctrine were discounted. In 1845 he published Organic Motion and Its Relation to Metabolism in which he gave full details of his work, including his declaration that all living organisms were, in fact, heat pumps. He also corrected his original value for both the mechanical equivalent of heat and the universal gas constant. His small calculation error had been due entirely to relatively inaccurate contemporary values for the specific heats of water. The current value for the universal gas constant is R = 8.3143 joules per kelvin per mole. Mayer’s 1845 value is within 0.5% of today’s accepted figure. It was one of biology’s greatest triumphs.