Re: first law of thermo

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

John Denker commented off-list but welcomed a response on-list:

> 1) I was baffled by the last sentence:
>
> >  It is common in thermodynamics to restrict consideration to processes
> >  that keep the mechanical energy of the system constant, so that the
> >  first term on the right-hand side can be dropped.
>
> Said first term is the kinetic energy of the particles.
> For an ideal gas, the kinetic energy of the particles is
> the whole story.  If this term is dropped, there is no
> baby, not even any bathwater.
>
> Is this a misprint?

Nope, it's just a problem of nomenclature. Here's the deal on two
ways to split total energy E into mechanical energy E_mech and
internal energy E_int:

(a) The mechanics way: E_mech = bulk translational KE = MV^2/2 (where
M = total mass and V = center-of-mass speed) and then E_int = all
remaining energy.

(b) The thermodynamics way: E_int = thermal energy and E_mech =
nonthermal energy.

In both systems of thinking I would call the KE of the gas atoms
internal energy. The real issue is what to do with the energy of
flywheels, springs, etc. Cue footnote 3.

> 2) More generally, formulating the first law (or any law)
> in terms of W+Q is a bad idea.
>
> You have correctly defined W in terms of the microscopic
> positions of pointlike particles, and the forces acting
> thereon.  But then a dilemma arises, because the grandeur
> and utility of thermodynamics comes from its applicability
> to situations where you do not know the microscopic
> positions of the particles.

I agree with you to some extent. Cue footnote 3 again.

The part where I appear to disagree however goes something like this:

(i) There are many problems where even though we don't know the
microscopic positions, we nevertheless have enough statistical
information to average over them. Example: I adiabatically compress
an ideal gas. I can calculate work = sum of microscopic forces *
microscopic displacements and get integral of -PdV.

(ii) In more complex situations, I can develop models that will allow
me to approximate the particle work. For example, Bernard and
Sherwood's "asperity" model for friction. Or the standard "rigid
block and unstretching string" model to compute the work done by a
string pulling a block.

(iii) Similarly, I can develop models for heating by conduction or
radiation say that will enable me to hide some of my ignorance about
the microscopics.

(iv) If all else fails, I can do numerical simulations of individual
gas atoms, or a solid tip in contact with a plane of atoms, or
whatever. Not simple and arguably no longer thermodynamics. But
doable subject to certain conditions.

My bottom-line when all is said and done is this. I think that what
most texts are doing with the work-energy theorem in mechanics, the
first law in thermo, etc is basically okay. Some clarifications and
interpretations and context helps the students, granted. But the
basic theory can all be put on some reasonable logical foundation. It
is not necessary to exacto-knife out the chapters on work & energy,
thermo, etc and replace them with our own handouts.

In my opinion and I'm open to being convinced otherwise, Carl
--
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/