Re: [Phys-l] energy is well defined

[Jeff Weitz <weitz@pipeline.com>]

Hi all,

I wrote:
> > How about defining "kinetic energy" as the work done to accelerate an object
> > from rest to a given speed?

And John Denker wrote:
> That doesn't work too well for photons.
>
> In my experience, it is relatively easier to understand energy as
> a whole -- plain old energy -- and relatively harder to understand
> the various categories and subtypes.
>
> In particular, it is easier to know the energy of a photon than to
> know what part of it is kinetic and what part is potential.
Now I'm responding:

I agree about photons.  This being February, photons are not uppermost in my
mind ;>)  I'd like to work out way to include the energy of a photon in the
"work done" framework.  Can we talk about work done accelerating a charge?
Work done on an electron when it moves to a lower energy state?  Radiant
energy?  This would be a third category in addition to KE and (delta)PE.
What do you all think about this?

John:
> So now (if you'll pardon my awkward phrasing) it's "ability to have been
> done by work".  
 
Me:
I'd go with just "work done"

John:
>    All this is predicated on students having a robust pre-existing notion
>    of "work" ... which is not always the case.

Me:
I suppose; I always stress work before talking about energy.

John:
>    There is a school of
>    thought that starts with energy and derives work from there.  There
>    are some applications, such as piloting an airplane, where it is
>    important to think about energy, but incomparably less important to
>    think about force dot displacement.

Me:
Right.  Well, I'm not in that school, I guess.  I agree about the pilot,
though.  There are plenty of situations in my course where we think about
energy without going back to F dot s.  But that doesn't change the fact that
we have the grounding in place.  Now and then, when we invoke enrgy
conservation, I can remind my students that it's all work done.
> ======
John:
> Once you adopt the work-in-the-past idea, can't you drop the restriction
> about "conservative" forces?
>
> There's lots of non-conservative force fields in the world.  Don't they
> do work, too?  
>
>    In particular, the "electric power" sold by the electric company is
>    almost always traceable to non-conservative fields in a dynamo
>    somewhere.
Me:
It seems to depend on how you define "system."  If a "non-conservative"
force does work on a system then the sum of KE and PE of the system will
change.  Isn't that why we call a force "non-conservative" in the first
place, though we don't define "non-conservative" this way?
> ------------------------------

Jack Uretsky writes:
> Hi Jeff-
> How do you describe what happens when I mix a kilogram of 79
> degree water with a kilogram of 40 degree water in an insulated container?
> Regards,
> Jack
I respond:
Damn.  Gotta be careful posting to this list.

The average translational kinetic energy of the molecules in the mixture is
less than for 79 degrees and more than for 40 degrees.  In this case it will
be exactly what it would be for 2 kg of water at a uniform 59.5 degrees.
The distribution of energies will be a little different immediately after
mixing that what it will be after a little time passes.  (and we can talk
about that)

We have a shortcut that includes specific heat that we can use to calculate
the temperature of a mixture such as this one.  The shortcut takes into
account the proportion of translational KE, rotational KE and/or PE in a
substance, as well as the number of molecules per gram of that substance.
This is an example of a situation in which we use a derived shortcut rather
than go back to fundamental principles to solve every problem.

What do you all think?

To both Jack and John,
I appreciate this exchange so far. It need not end here.  Thanks.

Best,
Jeff