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Fw: Internal energy



--------- Forwarded message ----------
From: Arnold Arons <arons@dirac.phys.washington.edu>
To: antti.savinainen@KUOPIO.FI
Cc: herbgottlieb@juno.com
Date: Fri, 3 Mar 2000 14:04:33 -0800 (PST)
Subject: Internal energy
Mr. Savinainen:

Herb Gottlieb has forwarded to me your question about thermal
energy. Let me indicate what I mean by the term when I use it in my book
and
in my article in the Dec. 1999 issue of the American Journal of Physics.

I mean to associate the term "thermal internal energy" with the
temperature increase of a system, in other words with the random motions
(translation, rotation, and vibration) of the consituents on the
microscopic
scale. One produces changes in thermal internal energy by transferring
heat
through contact with a higher temperature body, by work done on the
system
reversibly (as in adiabatic compression of a gas), or by dissipation of
mechanical work (as in frictional interaction) or of electrical work (as
in a
resistive circuit.) Since the language conventions have not been rigidly
crystallized, different authors may use the energy language in slightly
different ways, and one must infer what is meant by examining the
context. I
doubt that you will find a "solid definition" in the sense of a "correct"
universal convention.

To illustrate more specifically what I mean by the various other kinds
of internal energy listed in my discussions of the energy concepts,
consider
the following messy assembly: a large cart, resting on the floor,
contains a
pendulum suspended from the ceiling, a small cart connected to the wall
by a
spring, and a small cart free to roll on the floor and bounce off the
walls. (The free cart is initially in contact with the rear wall.) We
take our
system to be the large cart, its contents, and the earth. We now put work
into
the system by accelerating the large cart and its contents forward and
then
backward to a stop (in other words, we give it a shake.)

What happens within our system? The pendulum and the cart on the
spring acquire macroscopic vibrational energy. This is what I mean by
internal
vibrational energy in the writing to which you refer. The free cart
acquires
macroscopic translational kinetic energy and continues to bounce back and
forth between the walls. This is what I mean by internal translational
kinetic
energy. The wheels of the carts acquire macroscopic rotational kinetic
energy.
This is what I mean by internal rotational kinetic energy. With friction
present within the large cart, some of the work put into the system is
dissipated immediately as the internal macroscopic motions begin and goes
into
(microscopic) thermal internal energy. As the macroscopic motions run
down,
all the work input eventually ends up as thermal internal energy. If one
examines the vibrational motions at various instants of time, the
pendulum-earth sub-system reveals continual changes between gravitational
potential energy and translational kinetic energy; while the
cart-on-spring
sub-system reveals continual changes between elastic potential energy and
translational kinetic energy. All these macroscopic energies I take to be
forms of non-thermal internal energy.

Another illustration: Suppose we are charging a lead storage battery
adiabatically (i.e., no heat exchange with the surroundings), the battery
being taken as our system. We do electrical work on the system. Most of
this
work goes into the form of chemical potential internal energy. Some of
this
work goes into thermal internal energy associated with whatever amount of
resistive dissipation takes place. When we use the battery to run a
motor, we
get back the stored chemical internal energy minus the amount of
resistive
dissipation that occurs.

Another illustration: A cylinder is allowed to roll down an inclined
plane with some degree of slipping (i.e., not idealized, pure rolling.)
Our
system consists of the cylinder, the plane, and the earth. The internal
gravitational potential energy of the system decreases. The internal
translational and rotational kinetic energies of the cylinder increase.
The
thermal internal energy of the system increases through the dissipative
frictional effect determined by the amount of slipping that occurs.

Does this help clarify the issues you raise? All good wishes,

Arnold Arons