Modern Engineering Thermodynamics

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V most efficient =
P o
ρAC D
Summary 721
and beyond. The entropy balance and the second law of thermodynamics may well be the key to understanding
the fundamentals of both biomolecular and biosocial phenomena.
SUMMARY
Classical thermodynamics can be used to develop a fundamental understanding of the operation of biological
systems. The conservation laws of mass, momentum, and energy are all obeyed by biological systems. The
second law of thermodynamics seems to be critical in the understanding of the self-organization, growth, and
aging of these systems. It has been argued that evolution via natural selection would be impossible without
death; therefore, a death mechanism must be programmed into every living creature. On the other hand,
from a thermodynamic point of view, such an argument isnotnecessary.Alloneneedstodoistorecognize
that no real process is completely reversible and that the entropy production for any real process is a positive
finite value. Thus, the internal irreversibilities would eventually accumulate to the point of system failure, or
death.
The field of biological thermodynamics covers not only individual living plants and animals but also (in ways
that we do not yet fully understand) interacting groups of plants and animals, societies, corporations, and
nations. Just as a living animal is made up of billions of living cells, each with its own unique function and
characteristics, a society is made up of many unique living animals, each having its unique function within the
society. Thus, the first and second laws of thermodynamics have the potential to also be the basic laws of social
organization, and they may contain the key to the birth, growth, maturity, and decline of social structures.
Some of the more important equations introduced in this chapter follow. Do not attempt to use them blindly
without understanding their limitations. Please refer to the text material where they were introduced to gain an
understanding of their use and limitations.
1. The membrane potential E i at 37°C due to the presence of chemical species i is
E i ðat 37°CÞ = 26:7 millivolts . ðkgmole electrons/kgmole iÞ
ln c
io
z i c ic
2. The energy conversion efficiency of biological systems is
_W + d
mV 2
+ d
mgZ
dt 2g c dt g c
_Q
η E =
= 1 +
−dU/dt
−dU/dt
3. The basal metabolic rate per unit mass of a mammal of mass m is
BMR/m = 293ðm −0:25 Þ = 293
m 1/4
4. The heart rate (pulse) for mammals of mass m is
Heart rate ðin beats per minuteÞ = 241ðm −0:25 Þ = 241
m 1/4
5. The breathing rate for mammals of mass m is
Breathing rate ðin breaths per minuteÞ = 54:0ðm −0:25 Þ = 54:0
m 1/4
6. The critical buckling height of a tree with a base diameter d is
h critical = 68:0 d 2/3
7. The locomotion transport number T is
T =
P
wV
where P is the total power expended in the transportation, w is the weight of the system, and V is its velocity.
8. The velocity that produces the most efficient transport process is given by