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

[John Denker <jsd@av8n.com>]

On 01/07/2016 03:33 AM, Diego Saravia wrote:

> A carnot machine with a working fluid, and two heat repositories, only
> transfers heat between systems at the same temperature,

Not quite the same.  There has to be "some" temperature drop
across each heat exchanger, in order to persuade the energy
to flow in the desired direction.  The faster the engine goes,
the greater this drop must be.

As a pedagogical simplification you may decide you are not
interested in the heat exchangers, but you cannot pretend
they do not exist.

In the real world, for engines built out of real materials,
there are utterly nontrivial engineering tradeoffs involving
the efficiency, size, power-density, et cetera.

> you can study in thermostatics,  systems with several temperatures, if, the
> only way to transfer heat between them is at the same temperature

Using the same amount of effort, using the same techniques,
you can analyze the heat-leak systems I described yesterday 
01/06/2016 06:24 PM.  Actually it's significantly /less/
effort, because the apparatus is simpler, the state space
is smaller, and the thermodynamic "cycle" is simpler.

Just as you ignored the inner workings of the heat exchangers
in the Carnot engine, you can ignore the inner workings of
the filament that carries the heat leak.  The apparatus was
designed to make such details irrelevant.  If a student
asks about it, you can say hypotheses_non_fingo, which is
Latin for "I'm ignoring the question because the answer 
doesn't matter".

The idea behind hypotheses_non_fingo has been an important
part of modern science since Day One (Galileo, 1638).

    On the other hand, at a later date, if you wish, you
    can spiral back and analyze the heat-leak filament
    in detail.  Divide it in to parcels.  Each parcel is
    /very nearly/ in equilibrium with its neighbors ...
    just as the Carnot engine is supposed to be very 
    nearly in equilibrium with its heat baths.

    In case you hadn't noticed, I'm a huge fan of the
    spiral approach to teaching and learning.

The heat-leak apparatus is everywhere nearly in equilibrium.
So stop kvetching and analyze it already.




Person saying it cannot be done is liable to be interrupted
by persons doing it.                        (H.E. Fosdick)

We have already settled the principle of the thing; now we 
are just haggling over the price.     (variously attributed)