Modern Engineering Thermodynamics

704 CHAPTER 17: Thermodynamics of Biological Systems
WHAT IS KLEIBER’S LAW? Continued
10 3
10 −3
10 −6
10 0 10 −9
Warm-blooded organisms
Metabolic rate (kcal/h)
Unicellular organisms
Cold-blooded organisms
10 −9
10 −12
FIGURE 17.7
Kleiber’s law graph.
10 −12 10 −6 10 −3 10 0
Mass (grams)
10 3 10 6 10 9
WHAT DO A BANANA, AN ORANGE, AND A PERSON HAVE
IN COMMON?
According to a new study, all living organisms share roughly the same resting metabolic rate when body size and temperature
are taken into account. The finding suggests that widely diverse species burn energy in predictable patterns. “The [corrected]
basal metabolic rate of an apple or tree is remarkably similar to that of bacteria, which is remarkably similar to a
fish or person,” says James Gillooly, at the University of New Mexico in Albuquerque.
A comparison of the basal metabolic rates for a large number of warm-blooded animals from mice to elephants
and birds produced the following empirical correlation, called Kleiber’s law:
BMR = 293 m 3/4 (17.16)
where BMR is the animal’s basal metabolic rate in kJ/d, and m is the animal’s body mass in kg. Thus, the basal
metabolic rate per unit mass of the animal is
BMR/m = 293ðm −1/4 Þ = 293
m 1/4 (17.17)
and it clearly increases with decreasing body mass.
EXAMPLE 17.3
Determine the basal metabolic rate (BMR) per unit mass of an 80.0 kg adult human and an 8.00 gram mouse. Since both
are warm-blooded mammals, explain why there is a difference in these values.
Solution
The basal metabolic rate per unit mass of a warm-blooded animal is given by Eq. (17.17) as
BMR/m = 293ðm −0:25 Þ