The main problem with the argument below is that the occurrence of heat
transfer between subsystems implies that there is not a well defined
temperature of the overall system; therefore, the change in entropy
cannot be identified with the amount of heat transferred divided by a
temperature.
The statistical definition of entropy is still valid, and an analysis of
the system using the statistical definition shows that the second law of
thermodynamics is obeyed. This example demonstrates why the statistical
definition is more basic than the macroscopic thermodynamic definition
of entropy.
Daniel Crowe
Oklahoma School of Science and Mathematics
Ardmore Regional Center
dcrowe@sotc.org
-----Original Message-----
From: Forum for Physics Educators [mailto:PHYS-L@list1.ucc.nau.edu] On
Behalf Of Tom Wayburn
Sent: Wednesday, October 12, 2005 9:31 AM
To: PHYS-L@LISTS.NAU.EDU
Subject: [PHYS-L] How to convince a Second Law skeptic
<snip>
It is actually not difficult to see where the idea that entropy always
increases comes from. Some simple mathematics will show entropy always
increasing. The trouble is, that a logical error is being made in those
simple mathematics. Entropy is defined as the heat transfer in or out of
a
system, divided by the absolute temperature in the system at which the
transfer takes place. So the logic goes, that heat is transferred out of
one
system at a high temperature, into another system at a lower
temperature.
The same amount of heat is transferred, but the temperature of the
receiving
system is lower. With the same amount of heat being divided by a lower
temperature, the entropy of the receiving system is a bigger number.
Therefore it is said that entropy always increases. But a subtle error
has
been done here. You do not find entropy by adding entropy from one
system to
another system. To find what has happened to the entropy of the combined
systems, you must find the heat transfer over the boundaries of this
combined system. Heat flow from one part of the system to another is an
internal matter that is not important to the definition of entropy. All
kinds of internal heat transfer can be happening, but entropy is defined
as
the heat transfer in or out of the system. You simply cannot add
entropies
from two systems and claim that this says something about the combined
system. Once this problem is recognized, contradictions about entropy go
away. But basically, entropy is not really important to the discussion
of
order and life. As I wrote before, it is a useful number in dealing with
problems of heat transfer. I am not aware of any practical significance
to
the equation for entropy that does involve order. The only thing that I
can
see that it has done is confuse things.