From: khosrow@bach.sim.es.com (Khosrow Motamedi)
Subject: Physics, Matter, Temperature and Energy
Keywords: Thermodynamics
Organization: Evans & Sutherland Computer Corporation
Date: Fri, 2 Oct 1992 11:18:13 GMT

This is mostly for the benefit of Hooshyar and an attempt to answer his
physics question, but may also be of interest to others, especially those
following the Physics-1A thread.

The concept of temperature formally comes out of what is known as the 
"Zeroth Law" of thermodynamics which states that a single number, a scalar, 
assigned to each of a set of thermodynamical subsystems will be sufficient 
to predict whether or not the subsystems will be found to be in thermal 
equilibrium should they be brought into contact, and furthermore, if they 
are not in equilibrium, in which direction will the inevitable flow of
energy (heat) take place. We can state that if bodies A and B are each
separately found to be in thermal equilibrium with body C, then they will be 
in equilibrium with each other.

Therefore temperature may be thought of as a property of matter only insofar 
as the body of matter constitutes a thermodynamical subsystem, and without
thermal interaction between two such bodies temperature is meaningless.

To look at this mechanically, temperature is the vigor with which the 
molecules of matter are in motion. At absolute zero temperature (0 K) there 
is no such motion and entropy is zero. In fact, this is one of the forms of 
The Third Law of Thermodynamics. An alternative statement of that law is 
that a body cannot be brought to absolute zero temperature by any series of
operations.

The temperature and property of matter question may perhaps be answered by 
answering the following question which I will leave as an excercize to the 
reader:

Given that all innate properties of matter are inherent in its individual 
molecules, does a single, isolated molecule of matter have a temperature?

It would be absolutely wrong to think of temperature as energy as a poster
mentioned earlier. And to clarify a few other misconceptions of the same 
poster:

1. There really IS such a thing as temperature - it is a fundamental
   variable in thermodynamics.

2. It is NOT the same as heat.

3. Temperature and heat CANNOT be used interchangably. They are measured
   by two completely different instruments and in completely different units.
   Temperature is measured by a thermometer. I will leave the heat
   measurement instrument as a trivia question for the enthusiastic reader.

In fact, the following relationship exists between temperature and energy:

    dE = T.dS  or  T = dE/dS   where S is entropy and E is thermal energy

From this it is easy to see that an increase or decrease in energy need not 
result in a change in temperature if a corresponding change in entropy takes 
place as well.

As an example, if one were to take a system in thermal equilibrium (e.g. a 
bar of steel) and cut it in two halves, each half would still have the same 
temperature, but only half the energy content and half the entropy of the 
original system. 

In thermodynamics, temperature is what is known as an intensive variable, one 
which does not depend on the size of the system. Another such variable is
pressure. In contrast, variables such as volume and entropy are called
extensive variables which do depend directly on the size of the system.
Consequently, energy, in this case in the form of heat, being dependent on 
all four variables, becomes extensive and dependent on the size of the
system.

Boiling of pure water at a certain temperature (one may even call it 100 C) 
under 1 atm. of pressure is no more provable than the laws of thermodynamics
themselves, or a great number of natural phenomena for that matter. The Laws 
of Thermodynamics are a set of logical assumptions that have been extensively 
justified and confirmed by their empirical success, and not a single observed 
phenomenon has ever been shown to violate them. Nor has any prediction of an 
equally accepted set of laws been shown to be inconsistent with them.

The boiling of water at a sufficiently high temperature and a low enough
pressure is, however, PREDICTED by The Laws of Thermodynamics and OBSERVED to
be true and consistent by experimentation under fixed and known parameters,
which in turn serves to confirm the validity of the laws. In general, such is 
the method of science. No scientific law can really be proven in the sense 
that mathematical theorems are. That would require exhaustively performing 
absolutely *every* possible experiment - an impossible task to say the least. 
However, one can be trivially disproven. Only one inconsistent observation is 
often enough to destroy a scientific model or set of laws, or at the very 
least, significantly limit its extent and generality. The next best thing to
a rigorous logical proof, then, is the accumulated success of a model as a 
result of repeated experiments with consistent results, as well as consistency
with the implications of all other well-established and pertinent laws.

Einstein once stated that he would be willing to discard *any* set of laws
of physics, except the most fundamental ones, those of thermodynamics.

I hope this helps.

Regards,                 |    186,000 miles/sec, not just a good idea,
-Khosrow                 |                 it's The Law.


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