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Re: Energy



At 05:20 PM 9/21/01 -0600, Larry Smith wrote:

I don't think it is a minor detail if your students think "flow" means
moving matter and you define it as you did here on the list.

The "flow" definition I gave on this list is perfectly consistent with a
commonsense notion of how matter flows. It is also perfectly consistent
with a correct notion of how energy flows.

The details of how a bird flies are different from the details of how an
airplane flies. But we call it flying in both cases. The fundamental
parallels between the two cases are vastly more important than the nitpicky
differences.

Similarly, the details of how water flows are different from the details of
how energy flows. But we call it flowing in both cases. The fundamental
parallels between the two cases are vastly more important than the nitpicky
differences.

I simply asked if you tell your students what "flow" means when you use the
term vis a vis energy.

I never knew I had to tell them what flow means.

I can feel fairly comfortable with your argument about energy flow _if_ I
know that you are using the definition you gave here on the list; but you
also seem to agree with Jim that energy flow isn't stuff moving.

I'll not comment on what I think you think Jim would think.

I consider energy to be a particular type of incorporeal stuff. I consider
flow to be more-or-less a particular type of moving, although "moving" has
slightly different connotations than "flowing".

I have repeatedly formulated the local conservation law as
change(stuff inside boundary) = -flow(stuff outward across boundary)
in which the RHS quite explicitly refers to stuff flowing. I still
consider this formulation to be correct and clear.

I almost think you'd agree with each other if you could agree on the
definitions.

I haven't seen anybody offer a definition that conflicts with what I've
been saying. I've seen people say no, no, no, you're wrong, wrong, wrong,
but nobody has offered to do an experiment or a calculation that conflicts
with anything I have said.

Seems to me to be an argument about semantics and pedagogy, which is why I
keep asking how you tell your students about energy flow. What is in your
students' minds?

I don't know. The question has simply never come up. Outside the confines
of this list, I've never had anyone object to using a commonsense
definition of flow and applying it to energy. If I hadn't seen it on this
list, the question would have been inconceivable. I just assume people
have a commonsense understanding of certain things.

Suppose I utter the sentence "Some water flowed in through a hole in my
shoe."
I expect people to understand the concept of "shoe".
I expect people to understand the concept of "hole".
I expect people to understand the concept of "water".
I expect people to understand the concept of "flow".

I even expect people to understand that the concept of conservation, namely
that the increase in water in my shoe was balanced by a simultaneous
decrease in water just outside my shoe.

Could everybody give a formal technical definition for these
terms? Certainly not; writing definitions is hard. But folks can reliably
use these terms to communicate with each other, and that's good enough for me.

My goal is to write so that people who want to understand will
understand. If there are others who want to misunderstand, I'm sure they
can find a way to misunderstand; that's not my problem.

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

In more detail:

1) Let us consider magnetic field lines:

1a) Field lines are a perfectly terrible way of representing some important
properties of a magnetic field, notably the superposition principle.

1b) OTOH field lines are a useful way of visualizing *some* interesting
properties of a real magnetic field. You can use iron filings to decorate
the field lines of a real magnet. You can see them, and with your sense of
touch you can get a feel for the tension along each line and the repulsion
between lines. Without a real magnet, even a drawing of field lines that
are everywhere endless gives you some idea how a divergence-free field can
be laid out.

1c) If you want to get things exactly right, you have to use the equations.

2) In the same way, let us now talk about water, energy, water flow, and
energy flow.

2a) Water is a perfectly terrible representation for *some* properties of
energy. For instance, energy does not boil at 100C or anything like that.

2b) OTOH when it comes to the _flow_ properties of water and the _flow_
properties of energy, there is an extraordinarily close
correspondence. The continuity equation for flowing water has *exactly*
the same form as the conservation equation for energy. As Feynman was fond
of saying, the same equations have the same solutions.

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

Show some small children three cars:
-- blue Taurus
-- red Taurus
-- red Civic.

Ask if the first two are exactly the same. No, of course they're not
exactly the same.

Ask if the second two are exactly the same. No, of course they're not
exactly the same.

Ask if the first two are alike in some way. Yes, obviously they are nearly
identical.

Ask if the second two are alike in some way. Yes, obviously they are the
same color.

What is so hard about this? Energy flow and water flow have something
very, very important in common. Does that mean that they have all other
possible properties in common? Why would anybody be confused about that,
even for an instant?