> For what it may be worth:
>
> The first law of thermodynamics asserts:
> A.) The Principle:
> 1.) For every well defined system there exists an energy state function
> E(x1,x2 ...), a scalar quantity, where the xi are the appropriate state
> variables.
> 2.) The value of the state function E may change by means of energy
> transfers between the system and objects in its environment.
> 3.) These transfers are always such that the total energy E_tot of a
> closed super-system of such systems is conserved (fixed in numerical
> value).
That's the right approach.
Some comments:
I'd say it slightly differently:
a) Energy obeys a local-conservation law.
b) There is such a thing as a "thermodynamic state"
(not to be confused with a microstate),
depending on a smallish number of state variables,
and we know what the state variables are.
c) Energy is a function of the thermodynamic state.
Item (b) is far from trivial. It is often given
short shrift or not covered at all, which is a
shame. It's true in equilibrium. It's true
enough near equilibrium. Far from equilibrium,
all bets are off.
Figuring out what are the appropriate state
variables requires a modicum of skill and
judgement.
Item (c): see remarks for item (b).
==========
All this takes for granted a fairly sophisticated
notion of what "equilibrium" is. As an illustration,
imagine trying to study the temperature-dependence
of the voltage of a battery, using e.g. the
Clausius-Clapeyron equations et cetera. You need
to know the temperature of the battery. That implies
there is a timescale over which the "thermal" degrees
of freedom reach equilibrium. But be careful, because
over a longer timescale there is a super-equilibrium
which demands that there is no battery voltage at
all, because the battery reactions have all run to
completion.
Further remark: It is a question of taste as to
whether items (b) and (c) are considered part of the
first law, or lumped in with the zeroth law, or stuck
somewhere else.
Note (!!) how it is not necessary to mention "W" or
"Q", and it is most certainly not necessary to
describe "Q" in terms of flow across any boundary.
=====================
Carl asked:
> aren't reversible processes necessarily near equilibrium?
No.
Recall the previous example: A fuel cell. The
reverse of this is plain old electrolysis. The
forward and reverse reactions can be pretty close
to reversible. In practice they are much more
nearly reversible than any heat engine you're
likely to see. The efficiency of the fuel cell
is incomparably greater than what you would get
from taking the same fuel (H2 and O2), burning
it to make heat, and running a heat engine.
The reactants have a great deal of energy and
relatively little entropy. Burning gratuitously
creates much more entropy, and then later you
have to pay a terrible price to unload this
entropy (via the waste-heat exhaust port on
your heat engine).
If you try to guess the efficiency of the fuel
cell using the thermodynamic formula, based
on the highest temperature and lowest temperature
in the fuel cell, you are going to be wrong
by orders of magnitude. The W+Q law is misleading
or at best inapplicable. The real laws of
physics (conservation of energy and nondecrease
of entropy) remain true and applicable.
As another example: the biochemical reactions
that convert, say, glucose to ATP and vice versa
are much more efficient than you would think
if you considered them as heat engines that
"burn" the glucose.
There are many other examples of processes that
are reversible but not heat-based. Physics
works; W+Q doesn't.