Modern Engineering Thermodynamics

17.5 Metabolism 703
Table 17.3 Breakdown of the Contributions to the Basal Metabolic Rate of the Various
Organs of the Adult Human Body
Organ Mass (kg) % of Body Mass % of BMR
Liver 1.5 2.14 27
Brain 1.4 2.00 20
Heart 0.3 0.43 10
Kidneys 0.3 0.43 8
Muscles 30.0 42.8 26
Remaining body tissue 36.5 52.2 9
Total 70.0 100.0 100.0
Source: Reprinted by permission of the publisher and the author from Margen, S. Energy metabolism. In: McCally, M. (Ed.), Hypodynamics and
Hypogravics, 1968 ed. Academic Press, New York.
CRITICAL THINKING
The average basal metabolic rates per unit surface area for male and female humans are showninFigure17.6.Whydo
you think the values for females are less than those for males over their life spans? Also, why do these curves level off at
about age 20?
Measuring an animal’s metabolic heat transfer directly is called direct calorimetry. The technique is very difficult
to carry out because the animal’s conductive, convective, and radiation heat transport rates must all be measured
directly. This is commonly done by putting the animal in a closed box that has water circulating through all six
of its sides. If the outside of the box is well insulated, then an energy balance shows that all of the metabolic
heat produced by the animal ends up in the circulating water. However, virtually all metabolic measurements
done today use a method called indirect calorimetry, wherein the CO 2 production and the O 2 consumption are
measured instead. Generally, indirect calorimetric techniques are found to be as accurate as the direct techniques
and are usually considerably easier and less expensive to use.
The ratio of the number of moles of CO 2 produced to the number of moles of O 2 consumed during an indirect
calorimetry test is called the respiratory quotient (RQ), and its value depends on the type of food being metabolized.
For example, in the metabolism of 1 mole of a typical carbohydrate, glucose,
C 6 H 12 O 6 + 6ðO 2 Þ!6ðCO 2 Þ + 6ðH 2 OÞ
6molesofO 2 and 6 moles of CO 2 are involved. Therefore, the RQ of carbohydrate is 1.0. On the other hand,
the RQ of protein is 0.8 and that of fat is 0.7. An animal generally consumes a mixture of these substances, so
how do we know which value to use as the energy equivalent per liter of O 2 consumed? Tests show that, under
basal conditions, the RQ is approximately 0.82 (which is very nearly the average value for the RQs of carbohydrate,
protein, and fat), and it can be shown that this gives a mixture composition of these three substances that
corresponds to an energy equivalent of 20.2 MJ/m 3 of O 2 ,or20.2kJ/LofO 2 . Thus, if we measure the number
of liters of O 2 consumed per unit time by an animal in the resting state and multiply this value by 20.2 kJ/L
O 2 , we obtain the resting energy consumption rate (or basal metabolic rate) of the animal. In the case of a fasting
(starving) animal, which is living on the consumption of its own body fat and protein, the energy equivalent
per liter of O 2 consumed is 21.3 kJ/L O 2 .
WHAT IS KLEIBER’S LAW?
In 1932, Max Kleiber (1893–1976) published a paper, “Body Size and Metabolism,” which included a graph (Figure 17.7)
that showed that an animal’s metabolic rate scales to the three-quarter power of the animal’s mass, or BMR ∝ M 3/4 . Kleiber’s
law has been found to hold across 18 orders of size, from microbes to whales.
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