Re: ENERGY WITHOUT W and Q

["Carl E. Mungan" <mungan@USNA.EDU>]

Ludwik wrote:

> It seems to me that most recent disagreements come from
> attempts to defend the First Law as dU=Q+W. Here is
> how Feynman described this law without Q and W.
>
> "There is a fact, or if you wish, a law, governing all natural
> phenomena that are known to date. There is no known
> exception to this law ? it is exact so far as we know. The
> law is called the conservation of energy. It states that there
> is a certain quantity, which we call energy, that does not
> change in the manifold changes which nature undergoes.
> That is the most abstract idea, because it is a mathematical
> principle; it says that there is a numerical quantity which
> does not change when something happens. It is not a
> description of a mechanism, or anything concrete; it is
> just a strange fact that we can calculate some number and
> when we finish watching nature go through her tricks
> and calculate the number again, it is the same."
>
> What he is saying, in my interpretation, is that U, the sum
> of all known forms of energies, remains constant. Some
> components of the sum decrease while others increase
> but U remains the same. That is the principle we use in
> solving some physics problems. Why is this not enough
> for the first course?

That form of the First Law is only useful for an isolated system.
Obviously the energy of an open system is *not* constant. We need
some way to discuss the mechanisms for changing the energy of a
system. This is what Q+W represent: two different mechanisms for
doing that, i.e. for changing the energy of a system.

But since energy is conserved globally, if we change the energy of
system A over here, by "doing" some combination of Q and W to it, we
must have changed the energy of system B by the negative of that
amount (if only A and B interact). In fact, I would argue (using defn
1 of heat) that we do the negative of Q and W *separately*.

I have said this before, but I consider that there are 3 central
concepts we want to teach. I would teach them in the following order,
though not necessarily sequentially.

Chap 1. Work and energy in a mechanics context
Here I think it is helpful to introduce pseudowork. Why? For 3 reasons:

(i) It is simply an integral of Newton's second law so it follows
*logically* and *immediately* from what the students just learned. I
here disagree 100% with Joe Heafner when he said "Let's pick ONE
SINGLE CORRECT defition and trash the rest." Teaching is progressive.
My view is we should start with a simple definition even if it is not
universally applicable. It is far easier to generalize and amplify
later than to try to be all-inclusive from the beginning. My
contention is the thermodynamic definition of work is just not well
connected enough to what the students have been learning to be
introduced as the first topic in the energy chapter.

(ii) It is the simplest way to introduce kinetic and potential
energies in a natural way, rather than dropping them out of the sky.

(iii) It gets the students engaged in work-energy concepts in the
familiar context of mechanics problems.

The example from John M's postings about the rolling car example was:
"From the frame of the road, both the road and gravity
contribute to (what I like to call) the 'pseudowork' done on the
car. The contribution from the road is negative and the
contribution from gravity is positive, but the road's contribution
is larger in magnitude so the pseudowork is negative.
Accordingly, the bulk translational kinetic energy of the car
decreases."
This is very clear and easy for a student to understand after
Newton's laws. It is a *real* shame to omit it just because you don't
like the word "pseudowork". The name is not important; the learning
opportunity is.

Chap 2. General concept of conservation of energy
Here I go with Feynman's statement above. We introduce internal
energy and discuss electrical, chemical, optical, etc forms of
energy. I *might* allow thermal energy on this list but I would need
some persuading as to why this term is useful. What's wrong with
"kinetic and potential energies of the microscopic particles?"

Again, an excellent example from John's posting:
"From the frame of the road, only gravity does (what I like to
call) 'external frame-specific work.'  That work is positive and
can be shown to equal the change in the total energy of the car.
(Note that I do not consider gravitational potential energy to
'belong to' the car and that I *do* consider gravity simply to be
another external force on the car.) The car's total energy is the
sum of its bulk translational kinetic energy and its internal
energy.  In this case, the bulk translational kinetic energy
decreases and the internal energy increases, but the increase in
the internal energy is greater than the decrease in the bulk
translational kinetic energy."
A very clear expostulation of the general concept of energy
conservation. I find the name "external frame-specific work" to be
too much of a mouthful and would not use it. But again, it's not the
name that counts, but the concept.

Chap 3. Thermodynamics
Here I introduce heat and the First Law. And all manners of other
beasts that will give students nightmares on first encounter. Frankly
I hope they learn Chaps 1-2 above and don't expect much in Chap 3
beyond just *exposing* them to some ideas and terminology.

From John once more:
"Within the system of the car itself only the road does (what I
like to call) 'external system-specific work.'  That work is
positive and is equal to the increase in the internal energy of
the car."
This is the traditional thermodynamic analysis, where we are not
interested in mechanical energy.

To my tastes, I would delete John's additional analyses from the
frame of the truck. This is how I satisfy Ludwik's "less is more"
idea. I have one central idea to communicate in each chapter above. I
like the idea of revisiting the same problem in each chapter to see
different angles on it. I think there's *great* learning potential in
this.
--
Carl E. Mungan, Asst. Prof. of Physics  410-293-6680 (O) -3729 (F)
      U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu    http://physics.usna.edu/physics/faculty/mungan/