Modern Engineering Thermodynamics

17.7 Limits to Biological Growth 711
Then, the rate of total internal energy expenditure within the body is
− _W
_U body = =
ð Þ muscle
η T
−490 J/s
0:250
= −1960 J/s
Therefore, _Q = _U + _W = −1960 + 490 = −1470 J/s: Consequently, the time, τ, required to produce a change in the total
internal energy of the system that equals the energy content of one pint of ice cream (see Table 17.4) is
τ =
ΔU _U
body
=
− ð1 pintÞð2:51 MJ/pintÞ
−1:96 × 10 −3 MJ/s
= 1280 s = 21:3 min
Hence, the 490. N weight in this example must be lifted continuously at a rate of one lift per second until a total of 1280
lifts have been made. This is clearly a great deal of physical labor just to overcome the enjoyment of a pint of ice cream.
Note that only 25% of the energy in the ice cream gets converted into external work while 75% of its energy is utilized elsewhere
within the body to keep the circulatory, respiratory, and other subsystems operating and is ultimately converted into
heat inside the body due to the internal irreversibilities of these processes.
Exercises
16. If the muscle efficiency in Example 17.6 is 30.0% instead of 25.0%, how many lifts would be required to work off the
energy content of the ice cream? Assume all the other variables remain unchanged. Answer: 1540 lifts.
17. If the 490 N weight in Example 17.6 is lifted only 0.50 m instead of 1.00 m, how long would it take to work off the
energy content of the ice cream? Assume all the other variables remain unchanged. Answer: τ = 2560 s = 42.7 min.
18. Suppose the person in Example 17.6 consumes a cheeseburger instead of a pint of ice cream. Assuming all the other
variables remain unchanged, how long would it take to work of the energy content of the cheeseburger?
Answer: τ = 694 s = 11.6 min.
Physiologically, it is very hard to lose weight by exercising alone. Most of the weight loss that appears after
exercising is really water loss due to perspiration. Perspiration is a convection-evaporation heat transfer mechanism
that removes the heat generated within the body due to the biological irreversibilities of exercise. Its function
is to help maintain a constant body temperature. This type of water loss is quickly replaced in the meals
following the exercise and should never be considered as part of a permanent weight loss.
17.7 LIMITS TO BIOLOGICAL GROWTH
For purposes of simplification, consider living systems to have a characteristic length L such that their surface
and cross-sectional areas are proportional to L 2 and their volumes are proportional to L 3 . The most obvious
effect of size on animal evolution is the ability of an animal’s skeleton to support its body weight. The ability
of a leg bone to withstand direct compression loading is proportional to its yield modulus and to the crosssectional
area of the bone. Hence, the strength of a leg varies with L 2 . However, the body weight of the animalisproportionaltoitsvolume,whichvarieswithL
3 .Theratioofbodyweighttolegloadingthen
increases with the animal’s size, L. Clearly there exists an upper limit (dictated by the elastic properties of
bone) to an animal’s growth, where its legs can no longer support its weight. The giant dinosaurs of 100 million
years ago apparently evolved up to this critical size. Some aquatic dinosaurs were too large to leave
the water because without the buoyant supporting force of the water their skeletons could not support their
body weight.
Even more crucial to mobile land animals are the bending stresses developed in their bones during walking and
running. Small animals can run with very nimble and flexible legs while heavy animals like elephants must
walk stiff legged to minimize leg bone bending stresses.
The internal heat generated by biochemical irreversibilities in animals is proportional to the amount of tissue
present, and consequently, it varies with L 3 . The rate of heat loss by an animal depends on the convective and
radiative heat transfer mechanisms, whichinturndependdirectlyontheanimal’s surface area and, consequently,
vary with L 2 . Therefore, the ratio of heat generation to heat loss is proportional to L 3 /L 2 = L, and if an
animal’s size were to increase indefinitely, a point would eventually be reached where the animal would overheat
and die. Thus, at least two mechanisms provide an upper limit to the size of animals: the strength of their
supporting tissue and their ability to maintain a moderate body temperature.
The rate at which oxygen and food reach the body’s cells depends on the volume of blood in the circulatory
system and the pumping capacity of the heart. The volume of blood delivered to the heart is proportional
to the cross-sectional area of the aorta and, consequently, varies with L 2 , whereas the volume of the heart