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Re: [Phys-L] "the" system versus "the" environment ... or not



On 10/30/2013 04:28 PM, Bruce Sherwood wrote:
Not an unreasonable point to make, John, but I would think that when one
encounters the more complex situations you describe it would be a huge win
that the student already had a firm grasp on system/environment, and the
experience of analyzing various situations with different choices of
system,

Yes, but that wasn't the question I meant to ask. The question
was, is there any cost -- even in the simplest introductory
situations -- to renaming
system --> Region 1
environment --> Region 2.

and that it would not be difficult to build on that foundation to
consider multiple systems/regions.

Well, it is axiomatic in this business that everything is harder
than you would have guessed. Murphy was an optimist. Let me give
a specific example of what can go wrong. The "enthalpy" example
I mentioned in a previous note was not chosen at random.

Approximately every physical chemistry textbook defines the enthalpy
as
H = E + PV [1]

where H is the enthalpy of the SYSTEM, E is the energy of the SYSTEM,
V is the volume of the SYSTEM and ... wait for it ... P is atmospheric
pressure, i.e. the pressure of the ambient ENVIRONMENT. They don't
write it in symbols, but if they did, it would be

Hsys = Esys + Penv Vsys [2a]
^^^^
H1 = E1 + P2 V1 [2b]

I kid thee not. You can't make this stuff up.

Now any sane person would argue that enthlapy should be a function of
state, i.e. a function of the state of the SYSTEM, and therefore it
should be

H1 = E1 + P1 V1 [3]

but that argument is (a) unfamiliar and (b) unconvincing to some folks.

Now it turns out that for a simple two-region system, the third law of
motion pretty much guarantees that P1 is numerically equal to P2, so
equation [2] is not quite as ludicrous as it seems. However, the point
remains that "numerically equal in a special case" is not the same as
"conceptually equivalent always". In operational terms, equation [3]
*generalizes* a lot better than equation [2]. Yet [2] is what gets
taught.

The rubber meets the road in a three-region apparatus, such as the
aforementioned air-gun: propellant, piston, and ambient atmosphere.
Some of the customers are fundamentalists and literalists to a degree
that would put Scalia to shame. They write equation [1] and interpret
it in accordance with equation [2a], which in this case means

H1 = E1 + P3 V1 [4]
^^^^

since the environment is now Region 3. They apply this with a vengance,
even though the ambient enviroment is not even in contact with Region 1.
Wackiness ensues.

Please don't think I'm exaggerating. Actually I'm understating the
depth and breadth of the problems that sometimes come up. For
diagrams and additional discussion, see
http://www.av8n.com/physics/ballistic-snafu.htm

=====================

The root cause of the problem has got nothing to do with thermodynmamics
or energy or "systems" or subscripts. The fundamental problem has to do
with memorizing the /form/ of a formula without bothering to understand
the meaning.

As the saying goes, ideas are primary and fundamental, while terminology
is is important only insofar as it helps us formulate and communicate
the ideas. Well, in this case, a little bit of good terminology goes
a long way. Sticking in the explicit subscripts (as in equation [3])
makes it easier to get across the idea that enthalpy etc. are functions
of state, in this case functions of the state of Region 1.

The counterargument to what I am saying goes like this: In the
ultra-simple end-of-chapter problems, it doesn't matter, so we
can save time and effort by glossing over the specifics.

To that I respond, if the only objective is to get the numerically-
correct answer in the short term, then I concede that conceptual
details don't matter. In contrast, if the objectives include inculcating
correct concepts that will stand the test of time, then interpreting
equation [1] correctly matters a great deal. The concept of paying
attention to what's a state-function and what's not matters a great
deal.

[...] it would not be difficult to build on that foundation to
consider multiple systems/regions.

OK.

On the other edge of the same sword, the equivalent contrapositive
statement is even more interesting: If they can't handle a simple
three-region situation, they never really understood the two-region
situation.