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Re: [Phys-L] work versus mechanical transfer of energy

I’m sympathetic, but I think more should be said.

First, it doesn’t need to be a parcel of fluid. It could be a point mass.

Next, the key is the gravitational field. We could turn things sideways and instead have a Hookean spring. The left end is connected to a rigid wall. The right end is connected to a point mass. We now slowly pull the mass to the right. No net work is done on the mass because our applied force rightward is always balanced (to within an infinitesimal) by the spring force pulling leftward on the mass.

So what happened? My muscles lost chemical energy. I did work. But the point mass did not gain energy. No net work done on it. Instead the spring gained elastic PE 1/2 k x^2. This is analogous to gravitational PE mgy in John’s example. I did work on the spring. The point mass was just a mediator between the energy I lost and the energy the spring gained.

On another note, I think formula [1a] (plus any other terms to account for mass transfer, electrical work, etc) is called the thermodynamic identity and it only reduces to the first law of thermodynamics under quasistatic conditions, which is only an approximation. The identity is indeed just a Taylor expansion of the energy in terms of its relevant variables.

Heat and work are always useful in reversible processes. For irreversible processes, only special cases (such as a free expansion) permit a useful distinction between heat and work. If I slide a block across a rough table, there is energy exchanged between the block and table; there is no useful way to decide how much of that energy is “work” (due to motion of asperities) and how much is “heat” (as the block warms up and moves onto cooler parts of the table). Best in such a case to ditch those concepts and instead focus on energy, entropy, and other state variables. Heat and work have no intrinsic value or importance; some times they help us calculate what we really want to know (such as the final temperature of an object) but when they don’t there’s no need to try to calculate them.

In my opinion, Carl

On Jan 6, 2016, at 1:36 PM, John Denker <jsd@av8n.com> wrote:

Hi Folks --

Consider the equation

dE = T ds - P dV [1a]
= "heat" + "work" [1b]
= thermal + mechanical ☠ [1c]

There are at least a dozen worse ways of writing that equation,
about 100 ways of misinterpreting it ... but that is not the
topic for today. I would like to point out that even under
the best and most generous interpretation, equation [1a] is
still not the whole story ... and the correspondence between
[1a] and [1c] is either wrong or highly misleading.

In particular, we must not equate "work" with "mechanical
transfer of energy".

Perhaps the simplest illustration is /hoisting/ a parcel of
fluid in a gravitational field. This can easily be done in
such a way that it does not change the temperature, entropy,
pressure, or volume of the fluid ... even though it does
change the energy. It is conventional and reasonable to
include the gravitational potential energy in the definition
of E.

The idea that we can raise the energy without doing work
on the parcel is consistent with the fact that there is a
work/kinetic-energy theorem ... not a work/total-energy
theorem.

Let's be clear: work is *not* synonymous with mechanical
transfer of energy.

It works better to write something like this:

dE = T ds - P dV + m g dh [2a]
= "heat" + "work" + "hoist" [2b]
= thermal + \---mechanical---/ [2c]

There are two "mechanical" terms. And we haven't even touched
on non-mechanical non-thermal terms such as µ dN.


This is a Big Deal because a lot of people take equation [1a]
to be "the" first law of thermodynamics, as if it were the 11th
commandment. Also, they define work to be mechanical energy
change. All that kinda maybe sorta works for selected examples,
but usually just spherical-cow-in-the-ivory-tower examples. If
you extend it to real-world situations, even rather simple real-
world situations, it's a disaster.

This is discussed in more detail, with a more-or-less unforgettable
diagram, at
https://www.av8n.com/physics/thermo/state-func.html#sec-e-other-variables

======

Partially tangential remark: None of the equations presented
above are the first law of thermodynamics. Not in practice,
not in principle, not even close. The first law should be
stated as conservation of energy, pure and simple.

Equations such as [1a] and [2a] are corollaries that depend
on a boatload of assumptions.

Furthermore, it is usually a mistake to focus on «heat» and
«work» anyway. If in doubt, if there is even the slightest
risk of confusion, forget about those concepts and instead
focus on energy and entropy.
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Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9b, 572C Holloway Rd, Annapolis MD 21402-1363
mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/