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A M . ZOOLOGIST, 8:71-81 (1968). Thermodynamic Considerations in Animal Nutrition RICHARD G. WIEGERT Department of Zoology, University of Georgia, Athens, Georgia 30601 SYNOPSIS. Acquisition of energy is a prime objective of the search for nutrition. The energy budget of a population or trophic level comprises the sum of energy gains and losses by each individual organism. Since these energy exchanges are governed by the same thermodynamic principles that govern purely physical transfers, the animal energy budget can be developed according to the Thermodynamic Laws. The following points are discussed in this paper: (1) Energetics at the organismic or population level can be completely described by equations based on the algebraic statement of the First Law of Thermodynamics (AE = Q + W). (2) Care must be used in the definition of terms such as enthalpy, entropy, and free energy. The latter two, particularly, have been misunderstood and misused in the ecological literature. Analogies between bound heat (TAS) and the respiratory heat loss (R) are misleading and logically unsound. (3) The possible advantage o£ using changes of free energy in ecological energetics is outweighed by the relative convenience and accuracy of methods for measuring changes in enthalpy. (4) There are theoretical errors in the use of respiratory gaseous exchange as an indirect estimate of metabolic heat loss by growing (as opposed to fasting) organisms. The acquisition of energy is a primary objective of the search for nutrition. Energy is defined as the ability to do work, and the performance of internal work is a necessity for the maintenance of the living state. Thus, energy is to the organism the means of continuing and expanding life; the means for maintenance, growth, and reproduction. I shall be concerned in this paper with "ecological energetics" as opposed to what might be termed "physiological energetics." The former encompasses the energy costs of the individual in a growing, reproducing population of organisms; the latter deals with the utilization of energy by the resting, post-absorptive individual. Some may consider the terms whimsical, yet the distinction is real and important for a clear understanding of just what the study of population energetics entails. From the ecological viewpoint the energy budget of a population comprises the sum of energy This paper is an adaptation from a manuscript chapter of a book on ecological energetics under contract to Reinhold Publishing Corporation. I wish to thank W. B. Cosgrove for reading and commenting on the manuscript. My own thinking on the subject matter of this paper has been aided by much discussion and comment on the part of graduate students who have taken the course in Energetics and Ecosystems. The figures were drawn by R. Rhindress. gains and losses by each individual organism. These energy exchanges are governed by the same thermodynamic laws that describe purely physical energy transfers and transformations. Discussion of the relationship between thermodynamics and animal nutrition requires consideration of the organism as a system; this, in turn, necessitates a clear understanding of just what makes a thermodynamic system and just how the concept applies to the energetics of the organism. In this paper I wish to make the following points: (1) energetics at the organismic or population level can be completely described by equations based on the algebraic statement of the First Law of Thermodynamics. (2) Thermodynamic terms such as enthalpy, entropy, and free energy, as well as energy budgets, have often been defined inadequately and used incorrectly in the ecological literature. (3) There is an advantage in the use of free energy instead of enthalpy in deriving energy budgets, since changes in free energy correspond most closely to the energy of potential use to the organism, but this advantage is far outweighed by the difficulty of obtaining free energy values as opposed to the convenience and accuracy of methods for measuring changes in enthalpy. (4) There are 71 RICHARD G. 72 of thermodynamic laws, however, and the seeming paradox is quite simply explained on the basis of the entropy value of the matter exchanged using the theorem of Prigogines (Bertalanffy, 1950). ENERGY ISOLATED OPEN WIECERT CLOSED MATTER FIG. 1. The three types o£ thermodynamic systems. possible errors involved in the use of gaseous exchange as an indirect estimate of the loss of metabolic heat by growing organisms. These have not been stated clearly, and the differences between the energetics of fasting vs. growing organisms have been ignored. THERMODYNAMIC SYSTEMS Development of a thermodynamic basis for an ecological energy budget requires treatment of the organism as a thermodynamic system. Such systems are of three types (Fig. 1): isolated—no matter or energy exchange with the surroundings; closed—energy exchange only; and openboth energy and matter exchanged. The energy relationships of living organisms usually can be considered only in terms of the thermodynamics of open systems, although certain experimental ecosystems can be sealed in glass and therefore constitute closed thermodynamic systems. A system must have defined boundaries; everything outside of these boundaries forms the surroundings. Because open systems exchange matter as well as energy with their surroundings, entropy and changes in free energy in such systems are difficult to evaluate. This difficulty has led to confusion regarding the relationship between classical (not statistical) thermodynamics and living systems. Some writers have even gone so far as to postulate that living systems repudiate the Second Law of Thermodynamics because of the possibility that they can do work and simultaneously exhibit a decrease in entropy. Living systems do not disprove the validity THERMODYNAMIC TERMINOLOGY There are two fundamental types of energy: kinetic, or energy of motion, and potential, the energy of position. Another and perhaps biologically more useful view of potential energy is that it is kinetic energy held in abeyance. Thus, we speak of the potential energy of a chemical compound, realizing that this corresponds to the same quantity of kinetic energy of molecular motion (thermal energy) if conditions were such that the "locked up" energy were released. Thus, matter has an "energy equivalent" depending upon what proportion of its total content of energy can be released under the stated conditions. Heat and work are two different ways by which energy may be exchanged directly between a system and its surroundings. Any one form of energy can be transformed into some lesser amount of work and transferred from the system, or it can be transferred completely as heat. Similarly, either heat or work received by a system may then exist as an increase in the potential, kinetic, or thermal energy of the system. Work operating against frictional forces is transformed into heat. Indeed, the degree to which a given amount of work is dissipated as heat (instead of being stored as potential or kinetic energy) is a measure of the irreversibility of the process. Highly irreversible processes are typical of living organisms (systems), therefore heat exchanges are quantitatively important in the energy budget. Because life requires work against frictional forces with a consequent heat loss, the organism, to maintain itself, requires a constant input of energy, even when the overall energy content of the living system is not increasing in any macroscopically observable manner. This constant input of energy necessary to just maintain the status quo forms a thermodynamic steady state. The amount of energy required for 73 THERMODYNAMICS AND ANIMAL NUTRITION this maintenance in relation to the energy content of the system is a measure of how far the system has departed from thermodynamic equilibrium, the condition of complete rest, or, for an organism, death! To summarize, the thermodynamic system represented by a living organism (or population) exchanges both matter and energy (heat and work) with its surroundings, represents a steady state (or some departure from this for a defined interval), and is highly irreversible, so that internal work is constantly being degraded to thermal energy and dissipated as heat. We can now develop the thermodynamic basis for the energy budgets of organisms or populations. ENERGY EXCHANGE AND THE FIRST LAW The First Law of Thermodynamics states, concerning the energy change of a system: AE = E2 - Ej (1) where: AE = change in energy content E, = initial energy content EL. = final energy content If for the present we disregard the possibility of exchange of matter, i.e., a closed system, equation (1) is restated as: AE = Q -f- W (2) where: Q = net heat-exchange with surroundings W = net work-exchange with surroundings Note that Ei and E2, representing the total content of energy of the system, include such energy quantities as the binding forces of the nuclei. Thus, although Ej and E2 could be evaluated only with difficulty, the change in energy content (AE) is measured with relative ease provided the type of energy transfer is known. For consideration of an energy balance in the living system, however, AE has a disadvantage. The living organism for the most part exists under conditions of con- stant pressure.1 A part of the work available for maintenance and growth will be absorbed in effecting changes in volume against this constant pressure. Such work is not useful in that it does not contribute directly to the maintenance of life. Rather, it is a necessary accompaniment of the work of maintenance. For this reason, biologists interested in the energy balance of organisms find it convenient to define the overall energy change of the system independently of the work involved in making changes of volume under constant pressure. The derivation of such a function is most conveniently illustrated by a mechanical system in which work of expansion is the only work done. In Figure 2, the cylinder and piston of area, A, initially define a system with volume, Vx. Imagine sufficient work expended within the system such that the piston is forced out against constant pressure P to define a new volume, V2. The force acting on the piston is of course PA and the pis/V 2 -VA The ton moves a distance V A ) work of expansion, PA X I ). = \ A / p (V, — Vj) — PAV, and Equation (2) is restated as: (3) AE = Qp + Wp - Wex where: Q P = heat-exchange at constant pressure Wex = work of expansion Wp = all other work (constant pressure) Substituting Wex = PAV we have: AE + PAV = Qp + Wp (4) or: (5) AH = QD + Wp = (AE + PAV) where: AH = change in enthalpy. If the change in volume is negative (con1 In this case heat lost from the system is considered negative and heat gained as positive. The same notation is followed in relation to work. Some algebraic formulations of the First Law use the equation A E = Q — W in which the work done on the surroundings is considered positive a.nd the work received negative. 74 RICHARD G. WIEGERT Q p + Wp) (7) AHm (change in enthalpy of matter) = H 2 — Hi (8) AHa = - (AHm where: Qp (net heat exchanged) = Q2-Q1 Wp (net work exchanged) = (9) (10) W2 — Wj Piston area = A Atmospheric pressure = P Wex= force x distance Force = PA V2-V, Distance = A W"ex ey= PA x V2-V| A = PAV FIG. 2. A simple mechanical system illustrating work of expansion. traction), then PAV is negative and AE is positive. Work is added to the system. Enthalpy (AH) is the overall change in energy of a system independent of the work involved in fluctuations of volume. Restating in the form of Equation (1) gives: AH = H 2 — Hi Thus the change in enthalpy of a system in which exchanges occur in both energy and matter requires modification of equations (5) and (6). The overall change in enthalpy of the system (AH6) results from the enthalpic change of the matter as it passes through the system (AHm) plus the net heat and work-exchanges. The enthalpic change of matter can be evaluated from a consideration of the initial and final states of the matter passing through the system, (H2 — Hx). The negative sign of AHm is necessary because a negative enthalpic change in matter resulting from passage through a system causes a net increase in the system-enthalpy (Hs). To avoid confusion the net heat exchanged and the net work exchanged are calculated using the same notation, that is (Q2 — Qi) and (W2 — Wx). In these cases, however, the subscripts do not denote initial and final but rather the total quantities of heat or work passing into or out of the system. Negative signs are necessary because a positive heat or work-exchange is a net loss from the system. Heat and work-exchanges do not depend (6) where: H x = enthalpy-content of initial state H 2 = enthalpy-content of final state. MATTER MATTER THE ENERGY BUDGET The open thermodynamic system represented by a single organism (or population) is diagrammed in Figure 3. The overall change in enthalpy of such a system (AHg) is given by: W2 W, WORK FIG. 3. The organism as a thermodynamic open system. 75 THERMODYNAMICS AND ANIMAL NUTRITION on the initial and final states but on the net rates of flux. Thus the overall change in enthalpy is based partly on measuring initial vs. final states and partly on measurements of rates of exchange. Of course we could look only at the initial and final states of the system and write: = HB - H . (11) but this would be less useful ecologically than substituting equations (8), (9), and (10) in equation (7) and writing: — Q2) (12) AH6 = (Hx (Wl-W2) Certain terms of equation (12) can be directly identified with those parameters common in animal energetics. For example, the overall change in enthalpy is readily equated with the chemical energy equivalent of production (growth or storage) over a given interval. (Note that the time interval must be short enough so that negative production can be detected). The term Hj — H 2 equals the difference between the enthalpy-content of ingested matter (I) minus that of egested and excreted matter (E). The value of (Qi — Qj.) equals the net heat lost as the result of the dissipation of internal work as heat (heat-loss of respiration or R). Under certain conditions the absorption or loss of heat by the organism due to direct thermal exchange with the environment may be large. However over the long term, heat exchanges of this type cancel (else the organism would continually increase or decrease in temperature to the point of death). The net exchange of heat is therefore negative, caused by heat losses associated with the high degree of irreversibility in living systems. The net work-exchange (Wt — W2) is generally negligible and is disregarded in most energy budgets. For treatment of the energetics of external work (work-output or W2) see Brody (1945). For all but domestic draft animals, external work, such as building of dams by beavers, piling up of sand by ants, etc., is but a small fraction of the internal work necessary for maintenance (dissipated as heat). Work done on the living system is rare and of little quantitative significance. Examples that come to mind are flying organisms lifted by the wind, aquatic organisms borne upward by currents, etc. Rewriting Equation 12 and omitting the term for work-exchange: AH8 = Hi - H 2 (Qx — Q2) (13) and comparing with the classical equation for the energy budget: P = I—E — R (14) where: P r= production-energy I r= ingestion-energy E = energy of egestion-excretion R = loss of respiratory heat the identities discussed above are immediately apparent. The energy budget is thus put on a sound thermodynamic basis, and, on the assumption that net work-exchanges between the living system and the surroundings are negligible, it quantitatively describes ecological transfers of energy. THE SECOND LAW OF THERMODYNAMICS In the preceding section considerations from the First Law alone were used to develop the equation for the energy budget. External work was ignored, and internal work, the work of maintenance of the living state, was considered only insofar as it was degraded by friction into heat and lost from the system. The capability of any particular energy input for performing work, as well as the necessary losses accompanying such a transfer were not considered. These are embodied in the concepts of free energy and entropy, terms whose definitions follow from the Second Law of Thermodynamics. Briefly, this law states that the transformation of heat (or any other form of energy) into useful work cannot be effected completely. A fraction is converted; the remainder is "bound" energy, the thermal energy of the final state, unavailable for useful work. This unavailable energy is the product of the capacity factor or entropy of the system times the absolute temperature. 76 RICHARD G. WIEGERT The relationship between free energy, TABLE 3. Thermodynamic values for the reversible and irreversible oxidation of glucose. Enthalpy and enthalpy, and entropy is found in the al- free energy values from Spanner (196S). Glucose gebraic statement of the Second Law. This in solid state, water in liquid state, gases at one aim pressure, and temp 25°C has had great utility in biochemistry and physiology for predicting the necessary conCo Hu, 0 0 + 6 0 2 H> 6 C02 + 6 H s 0 ditions and directions of spontaneous reIrreversibly, actions and in calculating the maximum Q, rr = —673kcal work potential. However, it is of little use Wmla= 0 for investigating the transfer of energy in AH = —673 kcal open systems, e.g., the organism and the Reversibly, population, primarily because unlike enQ rC v= +15 kcal thalpy, changes in entropy and free energy W n i I = —688 kcal AH = —673 kcal in biological steady-state systems cannot be Q r o r = TAS = " b o u n d " unavailable energy = + 1 5 measured directly. keal/mole The reasons for this are embodied in the definitions of these two terms, derived in a Qrov/T = AS = Entropy-change = + 0.050 kcnl/C mole brief, non-rigorous manner in the followW max = AG = change in Gibbs free energy = —688 ing section. For a thorough, biologicallykcal/mole oriented treatment of this subject the reader is urged to consult Spanner (1963). potential energy consists of one mole of FREE ENERGY AND ENTROPY glucose (CoH^Od). Because it contains poWe saw from the algebraic statement of tential energy such a system is capable of the First Law (5) that the overall change performing external work. Suppose the in enthalpy of a system was equal to the oxidation of the mole of glucose is comsum of heat exchanged and work ex- pleted under the conditions stated in Table changed. Obviously, the requirements of 1. If the reaction is conducted irreversibly the First Law could be satisfied by any and no work is produced, Qirr = —673 values for work done on the surroundings kcal and Wrain = 0. If, on the other hand, (external work) varying from no work the reaction is conducted completely re(Wmln) to some maximum amount (Wmax). versibly and all the potential converted to Furthermore, the maximum output of use- work, the system would be capable of perful work of which the system is capable forming 688 kcal of work while suffering represents its work potential. This is the an overall change in enthalpy of only —673 kcal. The additional 15 kcal of energy were free energy of the system.2 For a given change in enthalpy, the out- reversibly absorbed from the surroundings. Because we defined Wmnx as the free enput of work will depend, of course, on how ergy of the reaction we can now state that reversibly the reaction is conducted, i.e., how important are frictional losses and the free energy change of the oxidation of how closely equilibrium is approached. A glucose under the conditions stated is —688 given reaction conducted in a completely kcal/mole. If conducted reversibly, all the irreversible manner will result in no work free energy can be converted to work, and (Wmtn) although all the work potential 15 kcal of heat reversibly absorbed from (free energy) will be lost. In such a case the atmosphere will be upgraded to work. the heat loss will equal the change in en- The price paid for this conversion of heat to work is a loss in the work potential of thalpy. Consider a closed system whose chemical the system. Note from the reversible reaction shown in Table 1 that although the 2 For simplicity this discussion disregards any system lost only 673 kcal of actual energy work of expansion or contraction. We are, thus, (_688 kcal -)- 15 kcal), die loss of free ener concerned with changes in Gibbs free energy (AG) gy (Wmai) w a s 688 kcal. It is important instead of AF. Gibbs Tree energy, thus, bears the to realize that this difference between AH same relation to AF that AH does to AE. THERMODYNAMICS AND ANIMAL NUTRITION and AG does not represent an actual loss of energy. The energy is present as part of the thermal energy of the system, but since it is at the same temperature as the surroundings it is not available for conversion to work. Only by bringing the surrounding temperature below that of the system could some of the thermal energy be extracted and converted to work. It should be intuitively obvious that placing the system in surroundings of lower temperature will be easier the higher the temperature of the system. Conversely, we can reason that the relative unavailability of a kcal of energy absorbed by a system and held as an increase in the thermal energy will decrease as the temperature of the system increases. Thus, instead of using Qr(lv as a measure of the degree of irrevocable change taking place in a reaction system, we divide the heat reversibly absorbed, by the temperature of the system in degrees Kelvin (T). This measure is the change in entropy undergone by the system (AS). The actual heat exchanged (the increase in bound energy) is thus TAS. Equation (5) is now rewritten as: AH = AG + TAS (15) where: AG = Gibbs free energy change TAS = change in unavailable energy This is the algebraic statement of the Second Law of Thermodynamics. It states that for an isolated system undergoing a spontaneous reaction, e.g., one which can be harnessed to do work, TAS will always be positive. Furthermore, the Second Law of Thermodynamics states that the work done by a reaction system can never be greater than AG, and will equal AG or VVmo only under the ideal conditions of complete reversibility. Since the latter cannot be achieved in practice, we realize that a system cannot achieve 100% efficiency in the conversion of free energy to work. The difference remains as an increase in the thermal energy of the system. ENTROPY AND FREE ENERGY IN ANIMAL ENERGETICS Because a knowledge of the free energy 77 and changes in entropy of a reaction will determine its direction and degree of spontaneity, these functions are extremely useful to the physiologist or cellular biologist interested in the intermediary metabolism of an organism. Furthermore, if the balanced chemical equation of a reaction can be written, the necessary data can be obtained (for example, the calculations of free energy and entropy given in Table 1). There is, however, no direct way of measuring the free energy of biological material (Scott, 1965). Furthermore, the experimental determination of the entropy of material of unknown composition requires access to the necessary low temperature equipment. Despite the difficulties of determining these values there have been several attempts to apply the concepts of free energy and entropy to individual and population energy budgets. Scott (1965) used free energy values determined by difference between enthalpy and entropy to determine the thermodynamic feasibility of a given feeding pathway. Conceptually, his use of free energy in this way is correct. However, he concluded that some part of the energy of food would always be transferrable to the protoplasm of the feeding animal. This conclusion could have been reached on the basis of the Second Law, namely that a system possessing the capability for work can transfer energy to any other system. This fact limits the utility of free energy values in ecological energetics. A more serious and confusing use of thermodynamic concepts is the wholly erroneous notion that some sort of useful analogy can be made between the measurable parameters of the energy budget (I = P -|- R -j- £) and the changes in free energy and entropy. Equations (12) through (14) showed clearly that the proper identity is with the terms of the algebraic expression of the First Law. Nevertheless, a number of workers in animal nutrition and ecological energetics have tried to equate entropy with some part of the energy budget. Brody (1945) developed the idea of a formal anal- 78 RICHARD G. WIEGERT ogy between TAS and "specific dynamic action," the energy cost associated with the act of feeding. According to Brody, the energy budget for flow within an organism was: metabolizable energy equals net energy plus specific dynamic action. Metabolizable energy is the change in enthalpy of nutrient matter as it passes through the organism (calories ingested minus calories egested).3 Net energy is the free energy change, or the energy potentially available for the useful work of maintenance and growth of the organism. Although the value of TAS will certainly equal the difference between the metabolizable energy and the net energy, there is no logical reason to suppose it is estimated by measuring specific dynamic action. Indeed, the latter term is only defined on the basis of the difference in costs of maintenance energy between two different states of nutrition, fasting and feeding. In fasting, the intake of metabolizable energy is zero, as is the net energy, because there is by definition no input or output of matter. Brody was really concerned with the energy categories of feeds. Simply stated, we say that the digestive assimilative process of an organism is able to extract a certain fraction of the enthalpy from food as it passes through the body (metabolizable energy). The process of digesting and assimilating this amount of matter requires work (specific dynamic action), and therefore the apparent value of the energy assimilated must be reduced by the amount of work necessary to obtain it from the food, leaving a category of net energy. Thus, although metabolizable energy can be equated with change in enthalpy, for example see AHm, Equation (7), net energy is not the same as the associated change in free energy; Second Law considerations require for a spontaneous reaction a negative change in free energy larger than the value of AH. Further3 In common with many mammalian physiologists, Brody distinguished between energy of egestion (feces) and excretion (urine). However, for most groups oE organisms this distinction can not be made in practice, and the present paper considers egestion-excretion as a single term in the energy budget. more, T A S is the amount of heat bound as the result of change in the heat capacity of the system, not the amount of work necessary to digest and assimilate the metabolizable energy. On a more general level, Patten (1959) and later Wiegert (1964) attempted to develop analogies between the free energy equation and energy flow through organisms and populations. Aside from the technical error of defining TAS as gain in entropy instead of bound heat, there is, in addition, no justification for attempting to equate TAS with the respiratory heat loss of organisms. Scott (1965) has already commented briefly on the fallacy of this idea. The illogic of equating TAS with the heat loss from such a highly irreversible system as a living organism should be apparent from the earlier discussion and development of equations (12) and (15). The heat exchange between the system and its surroundings is identical with the change in entropy only under the special conditions of complete reversibility (QreT = TAS), and in this instance the organism would exhibit a net absorption of heat instead of a net loss. MEASUREMENT OF ENTHALPY In contrast to changes in free energy, changes in enthalpy can be evaluated from direct measurement of the heat evolved from a reaction conducted in a completely irreversible manner. The enthalpy-content of matter includes not only the chemical potential energy, but also the binding energy of the nucleus and lacks only that portion of the total energy content (E) represented by the work of expansion required to occupy the volume against the pressure of the atmosphere. Because the chemical reactions within the living organism do not involve any appreciable change in mass, it is customary with some authors to use Hcliem to distinguish the enthalpycontent of interest to biologists from the total enthalpy-content. This seems to me an arbitrary and unnecessary distinction, since the basic energy-yielding reaction is universally recognized as the oxidation of carbon compounds to carbon dioxide and THERMODYNAMICS AND ANIMAL NUTRITION 79 water. The energy resources of the organ- TABLE 2. Calculation of Aff from bomb-calorimetric of the example given by isms that do not utilize carbon compounds data (corrected version Scott, 1965). are usually of known chemical composition Heat of combustion = 4500 cal and values for enthalpy can be calculated N ga , = 0.0062 mole directly. R = 1.99 cal X "G"1 X mole"1 Measuring the chemical enthalpy of carPj = 29.72 atm bon compounds is usually done in a bomb P. = 1.0 atm calorimeter, although chemical wet-oxidaAH = heat of combustion + NgasKT In tive methods have been employed (Teal, = 4500 + (0.0062 X 1.99 X 29S) In 29.72 1957). = 4512 cal/g The theory of bomb calorimetry is well developed and has been discussed comprehensively by Sturtevant (1945). The sam- differs from the measured heat of combusple is oxidized in a rigid vessel containing tion (AE) by only 0.3%. The usual pracan excess of oxygen and the heat evolved tice is to omit this correction. For details is measured. However, enthalpy cannot be of corrections that are commonly made in equated directly with this heat, since the routine bomb calorimetry consult the Parr definition of change in enthalpy is based Manual #130 (1960). Finally, the preparation of samples on the assumption of constant pressure. This assumption is violated to some extent should be mentioned. To avoid decrease in calorimetric apparatus, thus introduc- of enthalpy either from loss of easily voing what is possibly the most serious error. latilized material (fats and oils) or from Nevertheless, the magnitude of corrections spontaneous changes in chemical composiis usually a small fraction (<1%) of the tion, the sample should be dried at as low total energy released. There are several a temperature as possible. Freeze-drying other sources of error, including the prob- is the method of choice. If this is not lem of trace elements other than carbon, feasible, then drying should be done in a hydrogen, and oxygen, the changes between vacuum oven at not more than 60° C. the initial and final states of the reactants INDIRECT MEASUREMENT OF RESPIRATORY or products, and technical difficulties in ENERGY LOSS measuring accurately the total amount of The loss of metabolic heat from the livheat released. These are covered in the ing organism can be measured directly treatise of Sturtevant. Scott (1965) gives a succinct discussion, (Brody, 1945) but the most common procewith an example, of the major corrections dures are indirect, usually involving the desirable for the calculation of AH from measurement of O2-consumption. The bomb calorimetry data. His example (with rationale for this choice as well as the reasome errors of his original text rectified) sons for choosing O2-consumption in prefis given in Table 2. The calculations are erence to CO2-production are beyond the scope of this paper (see Brody, 1945, or based on the relationship: Kleiber, 1961). However, indirect methods for the measurement of heat loss by other AH = AE + NRas RT X In (1VP2) (16) than fasting organisms involve a potential where: source of error that has never been stated explicitly. AE =r heat of combusion R = gas constant Equation (12) defines the heat exchange T = absolute temperature as (Qx — Q2) or, from Equation (14), as R. Ngag = change in moles of gas during To evaluate this parameter, the normal reaction procedure is first to measure the 02-consumption and, if possible the CO2-producP t = final pressure in the calorimeter tion. Because the ratios of CO2 produced P2 = atmospheric pressure The corrected value of A H , 4512 cal/g to O2 consumed (respiratory quotient or 80 RICHARD C. WIEGERT R. Q.) are known for the oxidation of carbohydrates, proteins, and mixed fats, measuring the nitrogen excreted and correcting the R. Q. for protein oxidized permits calculation of the proportions of fat and carbohydrate that were oxidized. Since the calorific equivalent of oxygen used in oxidizing each of these foodstuffs is known, the precise overall calorific equivalent of the oxygen used can be calculated (Brody, 1945). All of these computations, however, are based on the premise that the animal is in a fasting state, i.e., that no net production is occurring. When growth is taking place, however, the metabolic heat lost need not have the same relationship to the oxygen consumed as it does in the fasting organism. There are two reasons for this. The first, and perhaps quantitatively most important, reason is that the organic matter used as an energy source is not completely oxidized. Some of the elements go into synthesis of new organic compounds. If the carbon/oxygen ratio of the new matter is not identical with the original substrate, then somewhat more or less oxygen, as the case may be, is necessary for the oxidation of that part of the substrate material that is used to furnish energy for the synthesis plus maintenance-costs. The second reason involves the basic assumption underlying the indirect method of using Oo-consumption as an estimate of heat loss. This procedure depends on the degradation of all work to heat. In the fasting animal this assumption is met, since the only internal work done is that of maintenance, and all such work operating against frictional forces will ultimately be degraded to heat. During growth, however, a portion of the work will be conserved as an increase in the chemical potential energy of the material synthesized. The possible range of error introduced by disregarding the above factors in the indirect estimation of metabolic heat loss is illustrated by an elegant series of experiments by Battley (1960 a, b, c). By studying the energetics of yeast populations metabolizing a substrate of known composition and growing in a reaction vessel that permitted the direct measurement of the heat output, as well as the calculation of the O2 consumed and CO2 evolved, he obtained data from which the calorific equivalents of oxygen and carbon dioxide could be computed directly. Battley defined a non-conservative growth reaction as one in which no growth occurred and the substrate (glucose) was aerobically oxidized completely to CO2 and H2O (analogous to a "fasting" organism). He defined a conservative growth reaction as one in which the substrate was completely used up but only a part was oxidized, the remainder being used in the synthesis of new yeast protoplasm. In Table 8, I have used his data in the direct calculation of the calorific equivalent of the oxygen consumed in the complete utilization of one mole of glucose. For the non-conservative reaction the values are: O2 5.04 kcal/liter (S.T.P.) and CO2 5.04 kcal/liter (S.T.P.), with the R. Q. equal to 1.0. The change in enthalpy was calculated from the standard enthalpy of the reactants and products. For the conservative growth reaction, however, where one mole of glucose plus NH produced energy as well as yeast protoplasm (empirical formula CHX 71O0 4(1N0 17), the measured change in enthalpy was —479 kcal, the calorific equivalent of oxygen was 5.57 kcal/liter (S.T.P.), and that of carbon dioxide was 5.23 kcal/liter. In this case the R. Q. was 1.07. In this particular example, the second type of error, that due to work conserved as potential chemical energy, would have been canceled by the gross underestimation of heat output if the usual value of 5.00 kcal/liter of oxygen or carbon dioxide had been used. Unfortunately, no comparable data for multicellular animals are available. Accurate direct measurement of heat production by other than fasting higher organisms would require expensive, especially-designed equipment. Until such time as measurements of this type become feasible, or until empirical equations for the complex substrates and synthesized tissues of such organisms are available, calculation of the error involved in the indirect estima- THERMODYNAMICS AND ANIMAL NUTRITION 81 TABLE 3. Calculationx of the possible error involved in the indirect estimation of metabolic heal loss. The indicated calorific equivalents for oxygen, and carbon dioxide are those for non-growing (conservative) populations of yeast utilizing glucose aerobically. Data for ±H and empirical formulas arc from Battley (1960 a, b, c). Non-conservative Growth Reaction: Co H,. Oa (aq.) + 6O2 (aq.) -» 6CO2 (aq.) + 6H2O (liquid) Calculated AH — —677.2 kcal Calorific equivalent O2 = 5.04 keal/litor (S.T.P.) Calorific equivalent CO2 = 5.04 kcal/litor (S.T.P.) Conservative Growth Reaction: Co Hjs O6 (aq.) + 3.84 O2 (aq.) + 0.33 NH, (aq.) -> 4.09 CO2 (aq.) + 4.73 H.O (liquid) + 1.95 (C H,.71 O0.M N0.17) Pleasured AH — —479 kcal Calorific equivalent O. = 5.57 kcal/liter (S.T.P.) Calorific equivalent CO2 = 5.23 kcal/liter (S.T.P.) lion of metabolic heat loss of growing organisms or populations will be impossible. Perhaps it is sufficient at this time to recognize the possibility of such error and qualify accordingly any conclusions derived from calculations of the energy budget. Kleiber, M. 1961. The fire of life. John Wiley and Sons, New York. 454 p. Parr Instrument Company. I960. Oxygen bomb calorimetry and combustion methods. Manual 130. Moline, 111. 56 p. Patten, B. C. 1959. An introduction to the cybernetics of the ecosystem; the trophic dynamic aspect. Ecology 40:221-231. REFERENCES Scott, D. 1965. The determination and use of thermodynamics data in ecology. Ecology 46:673-680. Battley, E. H. 1960a. 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