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There's work, and then there's work



As a spin-off from another thread, let me explain my appreciation of the
differences in the use of the term "work" between

(1)the CM Work/KE theorem of mechanics, and
(2)the First Law of Thermodynamics.

(1) In the mechanical theorem, work = Fdx, where F is an external force
operating on the system and dx is the displacement of the CM of the system.
This external force accelerates the system center of mass; the numerical
values of the system's CM momentum and kinetic energy will in general
change. The mechanical CM Work/KE theorem establishes a numerical equality
between the integral of this CM external work and the increment in the
system's CM kinetic energy. This theorem is applicable to any particle or
system of particles/objects, without exception. It says nothing about
energy transfer or conservation, and is mute on the source/sink of the
system's kinetic energy increment - whether it is internal or external to
the system, etc. It is indeed remarkable that the external CM work integral
can thus monitor the CM kinetic energy increment with no knowledge of energy
sources, transfers or conservation. This theorem would still be valid if we
had to abandon our conservation of energy theorem; it is simply a
consequence of Newton's laws of motion.

(2) The First Law of Thermodynamics asserts the conservation of energy and
offers a general taxonomy for numerically evaluating energy transfers
between the system of interest and external objects/agents. It asserts the
existence of a system energy state function whose value can be altered by
energy transfers with external objects. It acknowledges "heat" as a separate
form of energy transfer and represents the transferred energy by a separate
term "Q". Other forms of energy transfer are represented by a general term
of the form Ydz (unfortunately called "work"). Here Y is some intensive
variable of the system state function and z is an extensive variable, such
that Ydz is BOTH the increase of the system's energy and the loss of the
energy of an external object. (Of course, in practice Q or Ydz may be
numerically evaluated in terms of the behavior of the interacting objects).
Implementation of this scheme obviously necessitates a model of the details
of the interactions between the system and the external objects, with an ad
hoc specification of the energy loss/gains in terms of Y and z for each
phenomenon involved ( mechanical, electrical, etc). As in other accounting
procedures, there may be various, valid ways of partitioning the total
energy transfer among these different terms - even between the heat/work
distinction. What is important is that the model consistently accounts for
an energy balance. This requires a detailed model of the interactions FORMED
EXPLICITLY IN TERMS OF ENERGY TRANSFERS.

Note the qualitative difference: In (1) Fdx is simply "force times distance"
and only its effect on CM acceleration is acknowledged - energy as something
passing between objects (let alone conserved) never enters the picture.
OTOH in (2) the entire enterprise explicitly rests on the assertion of
energy transfer and conservation, and explicitly seeks in Ydz a useful
numerical model for an ENERGY TRANSFER.

Much confusion has resulted from using the word "work" to describe both Fdx
of (1) and Ydz of (2)
Some have even written that the CM Work/KE theorem of (1) is invalid and
should not be used because its Fdx work does not always describe an energy
transfer, as Ydz in (2) necessarily does by design. The CM Work/KE theorem
is a very useful calculational tool of Mechanics - it should not be asked to
do what it knows nothing of. Its work, Fdx, may in fact be useful in the
First Law of thermodynamics as a Ydz, evaluating an energy transfer; but
this is a separate question and must be answered by an ad hoc energy
transfer model of the phenomenon at hand.

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor


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