Just as in the experiment, the temperature of the body is a balance between the rate of energy production (in this case metabolic) and energy loss. For the body, important mechanisms of heat loss are radiation, convective heat loss to the air (the dominant mechanism in the experiment), and evaporation. READING 1
METABOLIC RATE: The Basal Metabolic Rate (BMR) is the rate at which the internal energy of an organism is decreasing when it is fasting and completely at rest [8]. The metabolic energy production in resting mammals is surprisingly constant when divided by their surface area. For instance, from a white mouse weighing 34 g to an elephant weighing 3700 kg, the rate only varies from 42 to 100 Wm2 .
If one makes a graph of the basal metabolic rate of mammals of various sizes as a function of the mass of the animal, one discovers that the metabolic rate (dE/dt) "scales" with mass M in accordance with the formula (dE/dt) = C M34where C 90 kcalkg34–day . Using this formula, one can compute rather accurately the metabolic rate of any size of mammal. The fact that dE/dt varies as M34 is called Kleiber's Law.
This is but one example of many such scaling laws in biology. For example, experimental measurements show that the height of trees is proportional to the two-thirds power of the diameter of the tree. The study of such scaling laws, and an effort to find theoretical bases for them, represents an active branch of the sciences of zoology and comparative physiology [8].
Kleiber's Law can be reproduced theoretically by making the following assumptions:
(a) All mammals can be represented as consisting of body parts that are cylinders of length l and diameter d.
(b) The limiting length of a cylindrical column that can support itself is proportional to the 2/3 power of its diameter, i. e., l d23 .
(c) Since all mammals have roughly the same density, the mass M is proportional to volume.
(d) The power output of a muscle depends on its cross-sectional area, P d2 . This is known as Hill's law of muscular power. Hill found that the strength of muscle fiber and the rate of contraction of muscles x / t varies little from species to species but that the number of fibers in the muscle is proportional to the cross-sectional area. Since power equals F x / t (F is the force), this implies P d2 .
(e) The rate of heat production dE/dt is proportional to the power output of the animal's muscles.
Using these assumptions, you can derive Kleiber's Law, dE/dt M34 .