Better to teach entropy before energy. Perhaps, way before.
Hi Folks,
How can you *start* with energy? No one knows what it is - according
to Feynman. Nevertheless, Feynmen continually makes remarks that reveal
the picture of his every day working model, which is that energy (at
least the energy we are going to be interested in) is something that has
the potential to produce work, which it pays for at the common
(one-to-one) rate of exchange, i.e., with itself. I would be interested
to see how an "energy-firster" would bootstrap energy: "Axiom 1: It is
assumed that at each point of the universe in space-time - and such
ancillary compact dimensions as are needed to account for the fundamental
forces - is defined uniquely a vector-valued function of n (?) variables
with at least three continuous derivatives that maps the point *onto* a
manifold in T4x(BVD) such that Properties A, X, and GZ hold except for
sets of measure zero, which have no more than a countable number of
cluster points in the neighborhood of a singularity as defined by Sard's
Theorem of the previous chapter; moreover, the Hausdorff dimension shall
not exceed ..."
As far as distinguishing energy from work and heat in the First Law,
the students will know the difference between a volume integral (in the
energy term) and a surface integral (in the heat term and work term).
Also, it would be nice if the First and Second Laws are written as a
single accounting equation. I'm sure everyone but the engineers has
given up on the idea that heat is the transfer of energy into the CV and
work is ... out. Have a heat in and a heat out term. In fact, have
as many as you please. Ditto work. In the inbound term, include
everything that comes in and distinguish types as much as it is useful to
do so, i.e., a separate potential energy of mass entering and kinetic
energy of mass entering.
I don't think the concept of enthalpy is so damn useful to anyone who
is not a power plant engineer. Do we really need to combine the
'thermal energy' of the mass entering with the injection work required
to get it in? The injection work is the energy transferred from the
surroundings to the control volume by virtue of mass entering the control
volume, which energy alters the control volume (or the contents of the
control volume) and is referred to as "work_in" or the analyst says,
"Work was done on the control volume or its contents to get the mass into
the control volume. This work is accounted for separately from work done
by electric power lines or reciprocating crankshafts and pistons in
cylinders or other turning shafts or moving ropes or belts. That is, for
work that will be charged to the system as an energy expense not a raw-
material expense or utility fluid expense, e. g. - a cooling water
expense.
In particular, for certain materials, this work might be in the form
of tension (in a thin wire, say) times change in length of the wire;
surface tension times a change in the area of a film, say; intensity (of
magnetic field) times change in the quantity of magnetism [nb: I say this
approximately and roughly because I don't want to mention all of the
variables and I have forgotten their meanings]; ... ; as well as ordinary
PdV work that 'happens' when water, entering the system at pressure P_1,
has to displace a volume dV that was in the pipe ahead of it (already in
the control volume) to make room for itself. The water doesn't change
temperature because of that work done on it. It is merely further into
the system than it had been previously.
At the other end of the pipe, however, the same or nearly the same
volume of water is finally being pushed out at a lower pressure,
assuming the pump is not between the entrance and the exit of the water.
[John M., what kind of work is this and what is its energy relation?
Don't tell me. I'll tell you ... soon. It will be a test. I
promised myself I would work on your paper today. ]
One last thought: One can define a thermal flux (which I forgot how
to do correctly); nevertheless, my flux is f =
{u(x,y,z,t),v(x,y,z,t),w(x,z,t)} at every point in space and time.
Integrate dQ/dt = the surface integral of f dot ndA over the control
surface (or some appropriate subset of it) w.r.t. time from t_1 to t_2
to get heat. One could account independently for thermal energy moving
around *inside* the control volume. It wouldn't be heat unless the
analyst wished to partition his control volume. I wouldn't care if you
broke it (the control volume) into finite elements and solved the
equations rigorously on each element by some sort of Galerkin method.
Gibbs meets Cray. "Mr. Gibbs, I presume."
I've said too much again, so I'll simply erase the rest.