340
9 Bioenergetics
9.9 An Introduction to Entropy
In this section, we will summarize the central ideas which led to the second law
of thermodynamics and the concept of entropy. In Sect. 9.10, the logic behind
the second law will be given. In the history of the subject, heat engines played a
central role. The heat from burning wood supplied the energy for the first steam
engines. Engines which required less wood to produce the same amount of work
were desirable. The advantage of engines to drive industry with reduced manpower
and replacing beasts of burden was evident. This impetus drove innovation and also
new thinking about how to make heat engines more efficient.
In the abstract, a heat engine is any system, running in a cycle, which converts
some fraction of the heat input into work output. If one imagines metabolic
conversion of carbohydrates into usable energy as a ‘burning’ process, then we are
heat engines.
In 1822, Sadi Carnot carefully thought through the behavior of a simple engine
which runs by extracting heat Q H from a hot reservoir at temperature T H , produces
work W , and expels heat Q C into a cold reservoir at temperature T C . Carnot used the
following observation, now taken as a form of the second law of thermodynamics:
Heat does not spontaneously flow from a colder body to a hotter one.
With this statement, Carnot proved that the most efficient heat engine is a reversible
one, i.e. an engine which, if carried in its cycle in reverse order, will have the same
values of Q H , W , and Q C , except reversed in direction. 25 The efficiency is the
generic term for what you wish to get out divided by what you put in. For a heat
engine, this is the work out divided by the heat in: E = W/Q H . Carnot showed
that the efficiency of reversible heat engine is the maximum efficiency of any heat
engine, and can be written in terms of the temperatures of the source and sink of
heat with the expression W/Q H = (T H − T C )/T H .
Later, William Thomson (Lord Kelvin) and Rudolph Clausius, following
Carnot’s work, concluded, among other things, that the efficiency of any engine
could not reach 100%. Their statements are now taken as another form of the
second law of thermodynamics:
No heat engine, running in a complete cycle, can convert all of its heat input into work. 26
Because of energy conservation, Q H = W + Q C . Thus we can present the
efficiency in the equivalent form E = 1 − Q C /Q H . As we will see from Carnot’s
analysis, all reversible engines, independent of how the engine is constructed, have
an efficiency given simply by E R = (T H − T C )/T H = 1 − T C /T H . Because this is
the maximum efficiency, there follows the relation
25 A heat engine run in reverse is a refrigerator.
26 From our microscopic perspective, a 100% efficient engine would convert the chaotic motion in
heat transfer into the coherent motion characteristic of work, with no other change occurring.
9 Bioenergetics
9.9 An Introduction to Entropy
In this section, we will summarize the central ideas which led to the second law
of thermodynamics and the concept of entropy. In Sect. 9.10, the logic behind
the second law will be given. In the history of the subject, heat engines played a
central role. The heat from burning wood supplied the energy for the first steam
engines. Engines which required less wood to produce the same amount of work
were desirable. The advantage of engines to drive industry with reduced manpower
and replacing beasts of burden was evident. This impetus drove innovation and also
new thinking about how to make heat engines more efficient.
In the abstract, a heat engine is any system, running in a cycle, which converts
some fraction of the heat input into work output. If one imagines metabolic
conversion of carbohydrates into usable energy as a ‘burning’ process, then we are
heat engines.
In 1822, Sadi Carnot carefully thought through the behavior of a simple engine
which runs by extracting heat Q H from a hot reservoir at temperature T H , produces
work W , and expels heat Q C into a cold reservoir at temperature T C . Carnot used the
following observation, now taken as a form of the second law of thermodynamics:
Heat does not spontaneously flow from a colder body to a hotter one.
With this statement, Carnot proved that the most efficient heat engine is a reversible
one, i.e. an engine which, if carried in its cycle in reverse order, will have the same
values of Q H , W , and Q C , except reversed in direction. 25 The efficiency is the
generic term for what you wish to get out divided by what you put in. For a heat
engine, this is the work out divided by the heat in: E = W/Q H . Carnot showed
that the efficiency of reversible heat engine is the maximum efficiency of any heat
engine, and can be written in terms of the temperatures of the source and sink of
heat with the expression W/Q H = (T H − T C )/T H .
Later, William Thomson (Lord Kelvin) and Rudolph Clausius, following
Carnot’s work, concluded, among other things, that the efficiency of any engine
could not reach 100%. Their statements are now taken as another form of the
second law of thermodynamics:
No heat engine, running in a complete cycle, can convert all of its heat input into work. 26
Because of energy conservation, Q H = W + Q C . Thus we can present the
efficiency in the equivalent form E = 1 − Q C /Q H . As we will see from Carnot’s
analysis, all reversible engines, independent of how the engine is constructed, have
an efficiency given simply by E R = (T H − T C )/T H = 1 − T C /T H . Because this is
the maximum efficiency, there follows the relation
25 A heat engine run in reverse is a refrigerator.
26 From our microscopic perspective, a 100% efficient engine would convert the chaotic motion in
heat transfer into the coherent motion characteristic of work, with no other change occurring.