9.10 The Laws of Thermodynamics
343
liquid. The newly formed crystals release heat. 29 The crystal subsystem has less
entropy than the originating molecules in the liquid. But because of the heat
released, the mixture of crystals and liquid has more entropy than it had as a pure
liquid. An egg becomes a chick by natural processes. The chick has far less entropy
than the original material in the egg. But during development, the growing embryo
releases heat into the environment, making the sum of the entropy released to the air
and the negative entropy produced in the chick still positive. A chicken egg MUST
expel more heat than it takes from the mother hen if the egg embryo is to develop! 30
9.10 The Laws of Thermodynamics
Those are my principles. If you don’t like them, I have others
—Groucho Marx
The laws of thermodynamics apply to macroscopic systems, which are systems
with a large number of entities, such small subsystems, sharing the available energy
through quasi-random processes which are allowed to distribute that energy among
the possible microstates of the system. The first law is simply energy conservation.
The total internal energy of a system is designated E. Expressed microscopically,
E =
n k k
(9.26)
where k , an “energy level,” is one of the energies (both kinetic and potential)
available to the entities in the system. The energy levels are labeled by an index
k = 0, 1 2, · · · . The n k , are the “occupation numbers,” giving the number of entities
which have the designated energy k . For example, in a biological system, there
will be lots of water molecules in their ground state, whose energy we might call
water
o
. For a tiny biological cell, the corresponding occupation number for water
molecules in this state will be astronomical, perhaps n water
0
≈ 10 14 . The system
energy can change by changes in the occupation numbers (a “re-population”), by
a shift in the energy levels themselves, or both. A shift in the energy levels can
be caused by a change in the forces exerted on the system. A re-population of the
levels can be caused by a chemical reaction, or by contact with another system at
a different temperature. In the first case, the changing forces cause a change in the
strains within the system, and work is exchanged with the environment. The second
case defines heat exchange with the environment of the system. Formally,
29 Sodium acetate acts this way and is used in pocket warmers.
30 This is a surprise to many people, because they thought the hen was supplying heat! Instead, she
keeps the embryo warm, but the embryo gives more heat than the hen does.
343
liquid. The newly formed crystals release heat. 29 The crystal subsystem has less
entropy than the originating molecules in the liquid. But because of the heat
released, the mixture of crystals and liquid has more entropy than it had as a pure
liquid. An egg becomes a chick by natural processes. The chick has far less entropy
than the original material in the egg. But during development, the growing embryo
releases heat into the environment, making the sum of the entropy released to the air
and the negative entropy produced in the chick still positive. A chicken egg MUST
expel more heat than it takes from the mother hen if the egg embryo is to develop! 30
9.10 The Laws of Thermodynamics
Those are my principles. If you don’t like them, I have others
—Groucho Marx
The laws of thermodynamics apply to macroscopic systems, which are systems
with a large number of entities, such small subsystems, sharing the available energy
through quasi-random processes which are allowed to distribute that energy among
the possible microstates of the system. The first law is simply energy conservation.
The total internal energy of a system is designated E. Expressed microscopically,
E =
n k k
(9.26)
where k , an “energy level,” is one of the energies (both kinetic and potential)
available to the entities in the system. The energy levels are labeled by an index
k = 0, 1 2, · · · . The n k , are the “occupation numbers,” giving the number of entities
which have the designated energy k . For example, in a biological system, there
will be lots of water molecules in their ground state, whose energy we might call
water
o
. For a tiny biological cell, the corresponding occupation number for water
molecules in this state will be astronomical, perhaps n water
0
≈ 10 14 . The system
energy can change by changes in the occupation numbers (a “re-population”), by
a shift in the energy levels themselves, or both. A shift in the energy levels can
be caused by a change in the forces exerted on the system. A re-population of the
levels can be caused by a chemical reaction, or by contact with another system at
a different temperature. In the first case, the changing forces cause a change in the
strains within the system, and work is exchanged with the environment. The second
case defines heat exchange with the environment of the system. Formally,
29 Sodium acetate acts this way and is used in pocket warmers.
30 This is a surprise to many people, because they thought the hen was supplying heat! Instead, she
keeps the embryo warm, but the embryo gives more heat than the hen does.