Principles of General Physiology

The fact, derived from universal experience, that free energy always tends to diminish, if it possibly can, is sometimes known as the "principle of Carnot and Clausius." It was also enunciated, about the same time as the publication of the paper of Clausius referred to above, by Lord Kelvin (then Prof. William Thomson) under the name of the " Dissipation of Energy." The principle has obviously a great practical, as well as philosophical, importance. It has been made by Ostwald (1912) the basis of a general rule of conduct, which he calls the "Imperative of Energetics." The rule may be translated thus: "Waste not free energy ; treasure it and make the best use of it." As will be admitted, the admonition is an excellent one, and, when applied, leads to interesting results, as may be seen from the collection of essays under this name. To mention two subjects only, which are amongst those discussed, the waste involvedin war and the value of a universal standard for the sizes of printed books.

Another property of energy will be made clear by the following consideration. The work to be obtained from a stream of water depends not only on the height from which it falls, but also on the quantity of water flowing. A mere trickle, even from a considerable height, is of no practical use. Energy is composed, then, of two factors, which are known as the " intensity " and " capacity " factors. In the above case the distinction is obvious, height being intensity, and quantity of water capacity. In electrical energy, the intensity factor is difference of potential or electromotive force, while the capacity factor is current. In heat, the intensity factor is temperature, what the capacity is does not at once seem obvious. Sometimes the name "entropy" is used, as in the 0<f> diagram of the engineer, where one co-ordinate is the absolute temperature (6), the other (0) is the capacity factor, or "entropy," so that the area is the heat energy. It would be better, perhaps, to limit the word "entropy" to its original definition as given by Clausius. viz., the ratio of the "bound" energy to the absolute temperature.

Energy, then, is equal to a capacity factor multiplied by its appropriate intensity factor. It will be noticed that the intensity factors are what are called " strengths," whereas the capacity factors are of the nature of spaces or masses, so that the latter sum together when combined, while the former do not. If a litre of water at 50° be added to a second litre of water at the same temperature, the energy content of the mixture will be twice that of a single litre, due to doubling the capacity factor ; the intensity factor, temperature, on the other hand, is not altered.

The distinction between capacity and intensity factors appears to have been first made by Helm (1887). The considerations of this paragraph enable us to express the second law of thermodynamics in a new way, viz. : in a closed isolated system transference or conversion of energy can only occur when differences of the intensity factor are present. In ordinary cases of chemical combination, as is well known, additions are made by not less than one atom at a time ; similarly, electric charges on ions

are added or removed by units of one electron at a time. The question naturally arises, are there similar phenomena in the case of energy ? Now, in the consideration of the solid state of aggregation, certain phenomena have been met with which suggest that energy is dealt with in units at a time, in other words, that it cannot be divided into portions smaller than these units, called "quanta" by Planck (see p. 254 of Nernst's book, 1913). In the treatment of the solid state from the kinetic point of view, it is to be remembered that the molecules are only free to move or vibrate about a mean position, which does not change, contrary to what obtains in gases and liquids. Nernst (1913, p. 252) finds that the atomic heat of substances becomes very small as absolute zero of temperature is approached, and becomes practically nil at quite finite temperatures. In other words, the amount of energy imparted by the impact of vibrating molecules is not what the kinetic theory as applied to gases at ordinary temperatures would lead us to expect. The discrepancy is explained by the theory of quanta of Planck and Einstein, namely, that in the production of vibrations of an atom around its fixed position, as, for example, by the impacts of gas molecules, energy is taken up only in certain "quanta," and that these units are directly proportional to the period of vibration of the atom. For a freely movable gas atom this period is, of course, zero, so that in this case kinetic energy can increase steadily and the kinetic theory of gases remains unaffected. In the case of solids, a different state of things exists.

If this view be correct, it would follow that the curve giving .the energy content, or partition of velocities between the atoms, instead of being a continuous one, would rise in a series of equal steps, each corresponding to a quantum of energy. A certain formula expressing atomic heats has been deduced by Einstein from this point of view, and, in the experiments made by Nernst and his co-workers, it has been found to be confirmed in the case of eight distinct elements. It applies also to the experiments in which the atomic heat of salts was determined by making use of the optical measurements of absorption bands made by Rubens. The absorption bands are taken as representative of the vibration periods of the atoms. Further measurements will be found in the account given by Nernst (1913, pp. 254, etc.), together with more details of the theory itself than can be given here.

Practically all energy available in the animal body is derived from the oxidation of food, and is, therefore, of chemical origin. It is very important to remember that chemical energy is readily transformed into other forms, without necessarily passing through the form of heat. In the various forms of primary batteries, the electric current, derived directly from the chemical reactions taking place, can be used to drive motors without any further change. The experimental facts concerning the relation of the heat produced in the contraction of muscle to the external mechanical work done show that the energy afforded by the chemical changes cannot pass through the stage of heat, since the proportion of work to heat is too high. The "efficiency" of muscle as a heat-engine would be 27 per cent, to 30 per cent, or more, according to various experiments. This would require, by the second law of thermodynamics, in a heat-engine, a difference of temperature between " boiler " and " condenser " of such a degree as to be incompatible with the life of cells. This fact was familiar to Fick (1882, p. 158), who makes the statement that the "chemical forces " must be used directly for mechanical work, and at the present time no physiologist holds the view that heat energy is a stage in the process.

What are the capacity and intensity factors in the case of chemical energy ? Willard Gibbs (1878) suggested the name "chemical potential" for the latter, although "chemical affinity" is perhaps the better designation. This latter name, however, has been used somewhat vaguely. The capacity factor is clearly the quantity of a substance taking part in a reaction, that is the equivalent or combining weight, so that : — It may assist in understanding the meaning of chemical potential if we remember that, in a voltaic cell, chemical energy is directly converted quantitatively into electrical energy. Faraday showed that the quantity of electricity obtained is propoi tional to the amount of chemical change, so that the capacity factors of the two kinds of energy are proportional. Hence the intensity factors are also proportional, or electromotive force is a measure of chemical affinity. Faraday, therefore, was justified in regarding electrical force and chemical affinity as one and the same, as Mellor (1904, p. 26) points out.

Ostwald (1900, i. p. 249) regards chemical energy as being of as many kinds as there are elements ("Stoffe"). We have seen already how the intensity factor of energy in general never increases of itself; so that if the chemical potential of the products of a given reaction is higher than that of the reacting bodies, that is, when a substance is produced requiring to be supplied with energy, an endothermic reaction in fact, energy must be supplied from some extraneous source : it may be heat from neighbouring bodies or chemical energy from a concurrent reaction, involving fall of potential, in the same system. In the last case we have what is known as a " coupled reaction."

While, therefore, there is only one kind of temperature, or two kinds of electromotive force, positive and negative, which can be increased or diminished by altering the magnitude of the forces producing them, chemical potential cannot be increased directly by the fall of potential in another reaction with dissimilar components. Ostwald gives the following example : — Hydrogen peroxide is a body of higher potential than water or oxygen. Hence, in order to form it, the potential of oxygen must be raised, or the oxygen made "active." This cannot be done by smy or every kind of reaction providing energy in the system, the neutralisation of acid, for example, but must come from a reaction such as the oxidation of phosphorus, in which part of the oxygen taking part in the reaction is made active by means of energy derived from the other part of the reaction in which the potential of phosphorus is lowered by conversion to oxide.

The expression for the maximal work (A) of a chemical process is given by Nernst (1911, p. 658) as— where R is the gas constant, T absolute temperature, and K the equilibrium constant of a reversible reaction. All reactions can be treated as reversible. As it is put by J. J. Thomson (1888, p. 281), if we were able "to control the phenomenon in all its details, it would be reversible, so that, as was pointed out by Maxwell, the apparent irreversibility of any system is due to the limitation of our powers of manipulation." K, in the above formula, may be regarded as the ratio of two opposite reactions. It follows at once that the greater K is, that is, the nearer to completion the reaction proceeds in one direction, the greater the amount of energy available. In some cases we know the value of K, so that the free energy of the reaction can be calculated at once.

Nernst (1911, pp. 709-716, and 1913, pp. 741-753) has also put forward a new method which he thinks may lead to the determination of the free energy of any chemical reaction. Limits of space forbid its description here, and readers interested may consult the original (see also the work of Pollitzer, 1912). It is held by Wegscheider (1912, pp. 223-238) that the maximal work to be obtained consists of two parts, one which is only to be got by making it to overcome external pressure, and is zero at constant volume; the other can be obtained in other ways, as electromotive force, for example. He gives formula; for the minimum total work, for the electromotive force of chemical reactions, the dissociation of a gas, and a reversible gas battery.

We shall see in the next chapter how the surface of contact of a liquid with a solid, a gas, or another liquid, with which it does not mix, the interface between any heterogeneous phases, in general, has the properties of a stretched film. It can therefore do work when this tension is able to decrease. Now if we consider the energy available in a living cell, we see that, although chemical potential can exert its full effect in a small space, the capacity factor of chemical energy needs considerable active masses in order that much total energy shall be afforded. In surface energy, on the other hand, although the

intensity factor can change but little, the capacity factor (i.e., the area of surface) can vary very greatly within quite small spaces. Changes in the state of aggregation of colloids, by which their surface can increase or diminish a million fold, is, then, a potent factor in cell mechanics (see the remarks by Freundlich, 1907, p. 102). In the picturesque language of Clerk Maxwell (1876, p. 93) : "The transactions of the material universe appear to be conducted, as it were, on a system of credit. Each transaction consists of the transfer of so much credit or energy from one body to another. This act of transfer or payment is called work."

Now, as Benjamin Moore (1906, p. 1) rightly points out, it is just in this transfer of energy that the various activities which we recognise as peculiarly vital show themselves. The statement of Jennings as to the importance of regarding organisms as " dynamic " has been quoted in the preface to this book. In fact, a system in static equilibrium is dead. This fact, however, does not imply that chemical investigation of such system is useless. Valuable information as to the energy changes involved can be obtained by comparing the chemical constitution of cells before and after performance of work.

There are many phenomena known which illustrate the peculiar activity of bodies in the very act itself of changing their energy content. The state of activity which can be conferred upon oxygen, by the oxidation of phosphorus or benzaldehyde, for example, appears to be connected with its change from a bivalent to a quadrivalent element, by which it gains electric charge. The active properties, however, are only manifested during, or immediately after, this change. The participation of electric forces can be shown by the steam-jet method of Helmholtz and Richarz (1890, p. 192). When a jet of steam issues from a fine glass orifice, it does not condense, so as to be visible, for a centimetre or so from the orifice. If bodies causing the formation of gas ions, i.e., electrically charged molecules of gas, are brought into the neighbourhood of the jet, condensation occurs almost at the orifice itself, and the cloud becomes larger and denser. If a stick of phosphorus be brought near the jet, the effect is very marked. It was shown by the observers named that none of the chemical products of the oxidation of phosphorus have this property. The electrical phenomena are only to be seen during the actual oxidation process itself.

The active agent diffuses rapidly compared with currents of air ; for, in the dark, the luminous vapours can be blown aside, without affecting the condensation of the steam jet. It is interesting to note that one of the authors of this paper was a son of the great Hermann von Helmholtz. This son, who showed much talent, unfortunately died before his father. A remarkable fact of interest in the present connection was noticed by Straub (1907, p. 135) in the action of muscaririe on the heart of Aplysia. The drug, at first present in higher concentration in the fluid in which the tissue cells are immersed, passes in course of time into the cells, until equal concentration exists within and without. But, although the drug can be shown to be present inside the cells by their action on another heart, its effect on the heart in which it is contained is no longer manifest. It is only during the actual passage into the cell, while its potential, so to speak, is different on the two sides of the cell boundary membrane, that it shows its characteristic effects.

Mention must here be made of the opinion of some writers that there is a special form of energy to be found in living matter, which is called by them "vital " or " biotic " energy. This is supposed to be convertible into equivalent quantities of the ordinary forms of energy, chemical, electrical, thermal, and so on, and vice versa. It is clear that no decision on the question can be arrived at until we have some instrument by which "biotic" energy, or, at all events, its intensity factor, can be measured, as the electrometer measures electrical potential, or the manometer, pressure of gas or liquid. For the present the assumption is purely hypothetical, and, as it seems to me, devoid of any purpose. It is to be noted that the modern adherents of this doctrine do not postulate anything more than a quantitative relationship between "biotic" and other forms of energy; in other words, the principle of the conservation of energy is supposed to hold even here.

The tendency of science is to greater simplification of the forms of energy ; radiant energy has practically become a branch of electrical science, the inertia of matter has been explained by the properties of moving electrons, and Faraday had already felt the identity of chemical and electrical energy. It seems, then, somewhat retrograde to assume a new form of energy, especially as there is no urgent necessity for it. The resources of the known forms of energy are not altogether exhausted.

Further discussion of the application of the doctrine of energy to living organisms will be found in the essay by Zwaardemaker (1906). Warburg (1914, pp. 256-259) calls attention to the fact that many cells, such as those of the central nervous system, the fertilised egg-cell, and nucleated red blood corpuscles, use energy in considerable amount, as shown by their consumption of oxygen, although they do no external work. It is evident that energy is required for some cell processes. Warburg suggests that it may be necessary for the maintenance of the " structure " of the cell, in the sense of keeping apart substances, which would mix by diffusion, the preservation of the properties of semi-permeable membranes, and so on, all in microscopic dimensions, or less.

The complete oxidation of such substances as fats and carbohydrates sets free a large amount of available energy. If this energy is all converted into heat, for the purpose of measurement, it is possible to obtain a number expressing the total energy content of any oxidisable substance. Numbers obtained in this manner are known as "heats of combustion." They play a useful part in comparing the energy changes in various reactions. The usual methods of determining heats of combustion will be found in the textbooks of Physical Chemistry (see that by Findlay, 1906, pp. 245-263). The adiabatic calorimeter of Benedict and Higgins (1910) appears to be a convenient and accurate form of apparatus. The name "adiabatic" is used in general for any process in which no heat is allowed to escape or be taken in. A gas, for example, may be compressed under such conditions that the heat produced escapes as fast as it is formed, so that the temperature remains constant ; the process is " isothermal." If the heat produced by compression is prevented from escaping, the process is "adiabatic" and great rise of temperature may result. In the Diesel engine, the heat of compression is great enough to ignite the heavy oil used for combustion, although the process is not absolutely adiabatic, owing to cooling by the walls of the cylinder.

Heats of combustion, however, do not necessarily give the actual energy values of food-stuffs, as available in the organism. If converted into heat at once, only a comparatively small part can be utilised, even with large rise of temperature. Hence the importance of using the chemical energy of food in the way that will give most free energy. As A. V. Hill remarks (1912, ii. p. 511), " if it is shown that carbohydrate has, calorie for calorie of total energy, a higher proportion of free energy than fat has, this would have an enormous influence on theories of nutrition." This is given, of course, merely as an illustration of the necessity of due consideration of the difference between free and bound eneruv. In fact, Baron and Polsinyi (1913, p. 10), assuming Nernst's theorem (1913, p. 744), find that the free energy of the oxidation of glucose at 37° is 13 per cent, greater than the total energy, calculated from the heat of combustion. Heat must be acquired from surrounding bodies and converted to free energy.

Boltzmann, in one of his " Populare Schriften " (1905, p. 40), points out how the " struggle for existence " of living beings is not for the fundamental constituents of food, which are everywhere present in earth, air and water, nor even for energy, as such, which is contained, in the form of heat, in abundance in all bodies, but for the possession of the free energy obtained, chiefly by means of the green plant, from the transfer of radiant energy from the hot sun to the cold earth.

Boyle's law tells us that the volume of a gas is inversely proportional to the pressure, if the temperature is constant ; and the law of Gay-Lussac tells us it is proportional to the absolute temperature, if the pressure is constant. In symbols: — where V is volume, P is pressure, T is absolute temperature, and R is a numerical quantity, called the " gas constant," whose value depends on the units in which the other factors are expressed. This same law was shown by van't Hoff (1885) to apply to dilute solutions, and the theory of solutions based on the fact has had great effect on the progress of science. A portrait of van't Hoff in the year 1889 will be found in Fig. 23, in the year 1899 in Fig. 24. These portraits are given by the kindness of Prof. Ernst Cohen, of Utrecht.

When gases approaching their liquefying point, or concentrated solutions, are dealt with, the formula becomes more complex, since factors must be introduced on account of the molecules coming close together, so that their influence on one another, as well as the actual space they occupy, have to be taken into account. This question will be discussed in Chapter VT. In the present place, we will merely direct our attention to the expression which gives us the work done in compressing a perfect gas, or, by van't Hoff's theory, that done in concentrating a dilute solution. For simplicity, the temperature is supposed to be kept constant. This general equation will be found to turn up repeatedly in calculations involving considerations of osmotic pressure, such as the electromotive force of batteries, or the work done by the kidney.

Suppose, then, that we take a volume, v, of a gas at a pressure, p, and that we compress it so that its volume is diminished by a minute fraction of its original volume, that is by dv. The work done is pdr. Further, if we diminish the volume r.2, which is occupied by one gram-molecule, to ??,, the total work done (A) is the sum of all the minute portions, pdv, between the limits of these two volumes.- In the notation of the infinitesimal calculus : —

(Jorissen and Reicher, 1912, p. 35. Re- produced by the kindness of Prof. Ernst Cohen, Utrecht.) (Note that As a lengthened s, the first letter of sum, and is used to indicate the totality (Note here that R and T, being constants, are not subject to integration, which of course applies only to variables.) For the complete solution, the textbooks must be consulted, e.g., that of Nernst and Schonflies (1904, pp. Ill and 143) or of Mellor (1909, p. 254). A few words may perhaps be useful in enabling the reader to appreciate the meaning of the formula. The appearance of

(Repi-oduced by the kindness of Prof. Ernst Cohen, of Utrecht.) the logarithm is due to the fact that the differential coefficient of the logarithm of x to base and therefore, conversely, the integral of — is log, x, and that of — is log, v, or, when integrated between the limits of vz and vlt is Details of the way in which, by a simple application of the binomial theorem, the differential coefficient of a logarithm is obtained may be found in the books mentioned (Nernst-Schonflies, pp. 82-85, or Mellor, p. 51). We may note that the quantity e, chosen as the base of natural logarithms, is one of the most important in mathematics. As the sum of the infinite series : —

its value can be obtained to as many places of decimals as required. The differential coefficient of log x is the ratio of the amount by which log x increases when x increases by an infinitesimal fraction of its value, say it becomes x + h, to the increase h itself. That is, we want the value of °? ^ — _LL_°8j? when h becomes so small as to approximate to zero. When the expression is expanded by the binomial theorem, we finally arrive at another expression in which - appears multiplied by log e, i.e.,

There are many reasons for taking e, as the base of a system of logarithms in dealing with mathematical formulae, and when this is done, log e to the base e becomes unity. Our equation is then simply : — This digression into the region of pure mathematics is merely for the purpose of explaining the appearance of a logarithm in the expression for the work done in compressing a gas. Attention may be called to the frequent occurrence of processes whose magnitude at any given moment depends on how much of the process has been already completed, or, when an equilibrium is being approached, on the nearness to the end the process is. In the case before us, the work needed to cause the same actual diminution in volume of a gas increases the more the gas has been already compressed. Perhaps the simplest case is that of the absorption of light by a coloured liquid. Suppose that we allow 100 units of light of a certain wave length to enter the liquid and that, after it has passed through one centimetre, it has lost 0-1 of its original intensity and has become 90 units, or 100 x -9 ; after the next centimetre, this 90 units will have lost O'l of 90 and become 81, or 100 x 0'9 x 0'9, i.e., 100 x 0'92, and so on. Hence, after passing n centimetres, its value will be 100 x 0'9". Note that three layers do not absorb three times as much as one layer, but less, so that the value of the light transmitted is not 70 but 72'9. The application of this law (that of Lambert) will be found in the spectro-photometer, which has played so large a part in the investigation of haemoglobin.