Re: [Phys-L] ?conservation of _internal_ energy

[John Denker <jsd@av8n.com>]

On 01/14/2016 01:20 PM, Herbert Schulz wrote:
> Work isn't being done on the CM of the System (both boxes together)
> but certainly the spring is pushing against the spring in the red box
> and that box DOES move so the work done on it by the red box is
> non-zero. And visa versa.

Saying "certainly" is not a substitute for evidence, no
matter how many times you say it.

The red spring is not in direct contact with the blue spring.
At the only point of red/blue contact, at the only time and 
place where there is a force, there is no displacement.  The
blue pushrod does not move until contact has ceased and the
force has gone to zero.  There is no F·dx at the boundary
of the blue system.

The blue spring pushes only on stuff that is internal to the 
blue box.  Actions that are entirely internal cannot change
the energy of the system.

> Somewhere along the line you have to define `The System'.

When I draw a picture and then refer to "the blue box"
it leaves no doubt as to what system I am talking about.
  https://www.av8n.com/physics/thermo/state-func.html#fig-internal-energy-noncon

In any nontrivial thermodynamic situation, there will be
multiple systems, subsystems, regions, parcels, et cetera.
Results that apply only to "THE" one-and-only "SYSTEM"
are not usually worth very much.

In particular, to calculate F·dx you have to pick a
particular point and evaluate F and dx *at that point*
(and then sum over points if necessary).

> certainly the spring is pushing against the spring in the red box
> and that box DOES move

It is a fallacy to take the force observed at one point
on the box and combine it with the motion observed at 
some other point.

You can get the wrong answer to an enormous number of
questions that way.