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Re: [Phys-L] heat content



JD writes:
"We know this based on the usual definition of temperature:
dE
T := --------
dS | V

It looks to me like /any/ energy E will produce a nonzero
temperature T. So any energy is "thermal energy" "
***********************
Whoa ...!!!!
The dE in your statement does not encompass /any/ energy. There are other ways of changing E:
Even for the simple system which your equation considers, E = E(S,V,N) and the full story is-->

dE = (dE/dS_V,N)dS + (dE/dV_S,N)dV + (dE/dN_S,V)dN, or

dE = TdS + PdV + MudN, all three terms contribute to the system internal energy as thus defined.

This is an equation of THERMOdynamics and the E under consideration is just the internal THERMAL energy.
It does not consider, for example, the energy increase of a glass of water when I lift it onto a table top, or put it into bulk motion, etc.

There are system energy increments which do not contribute to the internal thermal energy and which are not addressed in the thermodynamic model of internal thermal energy. It is thus useful to distinguish thermal energy from the rest of the total system energy (including the "mass-energy" of the constituent particles).

-----Original Message----- From: John Denker
Sent: Tuesday, February 11, 2014 2:26 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] heat content

On 02/11/2014 03:44 AM, Bob Sciamanda wrote:
Neglecting quantum fluctuations, a system at the absolute zero of
temperature has no "thermal energy". Thermal energy effects a
non-zero temperature and phase changes.

Excellent! That really clarifies things.
That tells us what "thermal energy" is.

As a corollary, we know that "thermal energy" is the same
as "energy".

We know this based on the usual definition of temperature:
∂E
T := --------
∂S | V

It looks to me like /any/ energy E will produce a nonzero
temperature T. So any energy is "thermal energy" ... which
is one of the things I've been saying all along.

I'm assuming finite S and a few other mild assumptions.
You get phase changes for free if you know the energy
and temperature.

===========================
In the context of
dE = - P dV + T dS [1]
on 02/11/2014 10:07 AM, Jeffrey Schnick wrote:

The thermal energy appears on the left side of your equation 1.

By all that's holy, the LHS of my equation 1 is the plain old
energy E, not the "thermal" energy.

This is yet another way of arriving at a place we've been before:
Very often when people talk about "thermal energy" they have no
way of distinguishing it from plain old energy in general.

For more about the notation, meaning, origin, and limitations
of equation [1], see
http://www.av8n.com/physics/thermo/state-func.html#sec-deriv

===========================
On 02/11/2014 07:17 AM, LaMontagne, Bob wrote:

Steam tables are based on the repeatable relation between
temperature, internal energy and phase. "Thermal energy" is not part
of the tables.

Yes! Good point.

In addition, FWIW, my steam tables book tabulates /entropy/ as well
as temperature, pressure, specific volume, and enthalpy. This is
yet another hint supporting what I've been saying for years:
A) Don't bother trying to quantify "heat". Quantify the energy
and entropy instead.
B) Very commonly, when people talk about "heat energy" you can
just cross out the word "heat" and assume they meant "energy".
Ditto for "thermal energy". This is consistent with point (A),
in the sense that the "heat energy" is a subset of the "heat".


The book I'm looking at is
Keenan & Keyes (1936)
_Thermodynamic Properties of Steam_
_Including Data for the Liquid and Solid Phases_

I inherited this book from my father. He used it a lot. He used
it for things like, you know, steam engines. I don't use the book
much nowadays, partly because steam engines are not a big part of
my life, and partly because I have a computer program that coughs
up steam-table data whenever I need it.
_______________________________________________
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Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
http://sciamanda.com