Re: [Phys-l] Third Law of Thermodynamics

[John Denker <jsd@av8n.com>]

On 01/26/2011 03:17 PM, Fakhruddin, Hasan wrote:
> The Third Law of Thermodynamics states that it is 'impossible to reach absolute zero in a finite number of steps'.
> How can we explain this law to students at, say, AP physics level?

Well, the short answer goes like this:  Consider cooling
something off by a reversible process.  (An irreversible
process would only make things worse.)  We know (by Carnot's
celebrated argument) that any reversible process is equivalent
to a Carnot cycle.  And we know that the efficiency of a
Carnot-style refrigerator goes to zero as the bottom temperature
goes to zero.

That's the answer to the question, if I understand the intent
of the question.

====================

Beware that the question embodies a possibly false assumption
about the terminology, about the definition of "the third law".
There is a version of the third law that says the entropy of
any object goes to zero as the temperature goes to zero.

Beware:
  a) This "third law" is not equivalent to the statement (quoted 
   above) about the impossibility of cooling.
  b) This "third law" (despite its name) is rarely if ever true.

This "third law" plays a prominent role in /classical/ thermodynamics,
i.e. pre-1898 thermodynamics, because without it we would be unable 
to determine the absolute entropy (as opposed to mere differences 
in entropy).  Without it, entropy would exhibit a kind of gauge 
invariance in /classical/ thermodynamics.

This is IMHO a sufficient reason for not bothering with classical
thermodynamics, and sticking with a modern (post-1898) definition
of entropy, i.e. the /statistical/ definition.

The 1800s have been over for a while now.  Classical thermodynamics
has been obsolete for more than 100 years.