Download Thermodynamic Considerations in Animal Nutrition Department of

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. Growth-reaction equations for
Spanner, B. C. 1964. Introduction to thei moSaccharomyces cerevisiae. Physiologia Plantarum
dynamics. Academic Press, New York. 278 p.
] 3:192-203.
Sturtevant, J. R. 1945. Calorimetry, p. 311-434. In
Battley, E. H. 1960b. Enthalpy changes accomA. Weissberger, [ed.], Physical methods of organic
panying the growth of Saccharomyces cerevisiae.
chemistry, I. Interscience Publishers, Inc., New
J'hysiologia Plantarum 13:628-640.
York.
Baltley, E. H. 1960c. A theoretical approach to the
study of the thermodynamics o£ growth of Sac- Teal, J. M. 1957. Community metabolism in a
temperate cold spring. Ecol. Monographs 27:
charomyces cerevisiae (Hansen). Physiologia
Plantarum 13:674-686.
283-302.
Bertalanffy, L. von. 1950. The theory of open sysWiegert, R. G. 1964. Population energetics of
tems in physics and biology. Science 111:23-29.
meadow spittlebugs (Philaenus spumariiis) as
Brody, S. 1945. ttioeiiergetics and growth. Reinaffected by migration and habitat. Ecol. Monohold Publishing Corp., New York. 1023 p.
graphs 34:217-241.