Re: [Phys-L] heat content

[John Denker <jsd@av8n.com>]

On 02/10/2014 03:18 PM, Jeffrey Schnick wrote:
> I don't think you have to restrict the work term to zero to talk
> about increasing the thermal energy. 

I disagree.  This is not a matter of opinion;  The math 
backs up what I'm saying.  See below.

>  In terms of your example of the
> baby bottle, with some water in it, standing at rest on a table, if
> you tilt the nipple over by pushing the tip of it to one side without
> changing the orientation of the rigid part of the baby bottle you
> increase the elastic energy of the system, 

That's not a P dV term within the usual meaning.  Please
let's keep things connected to

     dE = - P dV + T dS                  [1]

If you have a good reason for departing from this, please 
explain.

In particular, if you wish to shift attention to the rubber,
please say so explicitly.  The thermodynamics of rubber, 
including both the F dx and T dS terms, is a staple of 
thermodynamic pedagogy:
  http://www.feynmanlectures.caltech.edu/I_44.html
Everything I've said remains true for this system.  It is, 
however, a separate system, separate from the milk in the 
baby bottle.

We can even consider the joint system if you insist, at the
cost of introducing additional variables.

> if you pick the bottle up
> and shake it rigorously for for a few moments and then set it back
> down you have increased the thermal energy of the system, and if you
> throw it across the room, starting from when you picked it up and
> ending before it hits anything, you have increased the kinetic energy
> associated with the motion of the center of mass of the object.

Also not P dV terms.

> Based on your equating it to "caloric" I think you have chosen a
> definition of thermal energy that is easy to criticize.

I haven't seen any physics-based criticism yet.  Equation [1]
is what it is.  The physics and the math say that if you give
me both a P dV term and a T dS term, then I can construct
thermodynamic /cycles/ including the kind of cycle used by 
heat engines.  I can integrate T dS around a closed loop and 
get a nonzero answer.  This guarantees that "heat content" 
cannot possibly be a function of state.  Whether you call it 
"heat content" or "thermal energy" or "caloric" makes no 
difference to the math or to the physics.

The picture you want to have in mind is the Escher waterfall:
  http://www.av8n.com/physics/non-grady.htm#fig-escher-waterfall
  http://www.av8n.com/physics/thermo-forms.htm#sec-unreal

Conversely, if the system is so cramped that the integral of
T dS is always zero (around any closed path) then the system
is so cramped that you cannot build a heat engine.  This is
a direct consequence of the laws of physics.  If you have a
counterexample to this proposition, please explain how it
works.  Please include details.  Just saying "shake the
bottle" does not suffice to tell me how (or even whether)
you intend to construct a heat engine.