Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: work and energy



At 02:01 PM 10/3/01 -0400, Carl E. Mungan wrote:
I just want a way of deriving the various work-energy relations which is
simultaneously sound and reasonably simple, if that is possible ...

A noble goal.

I hope I'm not opening too much of an old can of worms here.

Hmmmm. There's enough here to start three or four interesting discussions,
plus a couple of flame wars :-)

So here's my stab at it:

Start from the W-K theorem for a particle: W_net = delta K proven in
any textbook.

What's K? From context I'm guessing it's total energy or something like
that. But I've never seen K used to denote that.....

Since this is based solely on N2 plus definitions, I think we would
all agree it's perfectly general for a particle. (Nitpicks: N2
requires an inertial frame - assume the lab is. I haven't defined
what a particle is - take it to be electrons, protons, and neutrons
if you like and we'll ignore relativistic particles including
photons, okay? **)

Sum over all particles making up all objects in the system: sum
W_net_i = sum delta K_i.

Split the kinetic energy term into the collective (translational and
rotational) kinetic energy of macroscopic objects (define this to be
simply delta K)

Ooops, looks like a redefinition of K. Redefinitions drive students nuts.

and the remaining microscopic kinetic energy of the
constituents relative to their collective parts (delta K_micro).

The notion of "microscopic" doesn't lead to a satisfactory solution to the
problem at hand. At the microscopic level, you can't tell what's thermal
and what's nonthermal -- it all looks the same at the microscopic level.

Split the work term into work done by external forces and that done
by internal forces.

In the immortal words of Han Solo: I've got a bad feeling about this.

Split the external work into work done by "collective" forces (define
this total to be simply W) and that done by "random" forces (defined
to be Q). My thought here is that heat is just work done by random
molecular impacts, in contrast to the organized force on a piston,
say. But I could use help clarifying this. **

The following may be helpful:
http://www.monmouth.com/~jsd/physics/thermo-laws.htm

The goal thereof is to give a fast overview at the conceptual level; not
detailed, but modern and uncompromisingly correct.

Split the internal work into work done by conservative forces and
that done by nonconservative forces (call the latter quantity
W_int,NC).

Split the conservative internal work into the interactions between
the macroscopic objects (define this to be simply -delta U) and the
remaining microscopic interactions (defined as -delta U_micro).

Collect terms and rearrange to get:

W + Q = (delta K + delta U) + (delta K_micro + delta U_micro) - W_int,NC

This is a valiant effort to repair an equation that needs repair but
doesn't really deserve it. The W+Q equation is just a horror. Any repair
job will be outside the scope of an elementary overview, and AFAICT not
worth the trouble no matter what the audience. A major purpose of the
writeup cited above is to show how to get along without the W+Q equation.

....

Okay, fire away. Is this overview basically okay or completely
flawed?

It's a bold step in the right direction. It demonstrates a good feel for
where the repairs are needed. But IMHO an even bolder step is needed to
achieve the goal of simplicity, clarity, and correctness ... namely walking
away from the W+Q equation entirely.