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Re: New AP Physics Convention in Thermodynamics



At 07:48 2001/07/03, Jeff Weitz wrote:

Hi Everyone,

...

"Another change for 2002 relates to the sign convention used for work=
in thermodynamics. In thermodynamic equations, the symbol W will rep=
resent the work done on a system rather than by a system, so that the=
first law of thermodynamics will be written D U =3D Q + W. This chan=
ge makes the sign convention consistent with that used for work in me=
chanics, as well as with the thermodynamic convention used in most ch=
emistry and some physics textbooks."

At 07:58 2001/07/03, Oregn Quist wrote:

For example, is the dV in the work integral (for work done "on" the system)
now changed from negative to positive ??? Or vice versa ??

This goes against the standard mathematical dV representing an "increase" in
V.

My experience has been that most physics books write dU = dQ - dW, and most
chemistry books write dU = dQ + dW. I suspect the difference is a result of
historical point-of-view. One of the first practical applications of
thermodynamic theory was probably the refinement of the steam engine.
Physicist/engineers of that era were concentrating on the dW term (in
particular, how to maximize it for a given dQ). So it would have been a
"positive" thing for the system to do work on the environment, and it would
be natural to set the sign convention for dW to reflect this.

On the other hand, chemist/thermodynamicists naturally concentrate on the
exothermicity/endothermicity of the reactions going on in their test tubes.
Any work done on the environment in this context would likely be due to a
test tube exploding! This might be viewed "negatively" and in any case
would be exothermic, meaning that the system (test tube) is losing (again,
a "negative" idea) energy to the environment. So the traditional sign
convention used by most chemists makes sense in its own context. From a
strict energy inflow/outflow point of view, it is also more self-consistent
in that a flow of energy out of the system is negative, whether in the form
of mechanical work or heat ("heat", by the way, being whatever quantity is
depicted by the arrows pointing out of the high-T reservoir and into the
low-T reservoir in Halliday and Resnick; I don't want to rekindle the
heat-as-noun argument).

Most of my physics students have already had chemistry. So that they don't
become confused about the sign difference between their chem and phys
texts, I simply point out to them that it's a difference of viewpoint. This
is more educational than it sounds, because it awakens them to the concept
of energy _flow_ in thermodynamic processes and reinforces the necessity of
distinguishing between system and environment.

I believe the chemists agree with us that dV is positive when the volume
increases; they simply redefine work as -p dV. We do the same sort of thing
(introducing "arbitrary" negative signs) in physics; for example, we
conventionally place a negative sign in the definition of bulk modulus, to
acknowledge the inverse relation between pressure and volume. Most of us
have no problem explaining to our students the reasoning behind this
convention.

=====

Feynman's Rule of Signs: If you know that the sign [in your answer] is
wrong, change it! [A paraphrase; I forget the exact quote.]

--MB