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Re: [Phys-L] heat content

I don't think you have to restrict the work term to zero to talk about increasing the thermal energy. 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, 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. Based on your equating it to "caloric" I think you have chosen a definition of thermal energy that is easy to criticize.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of John Denker
Sent: Monday, February 10, 2014 4:40 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] heat content

On 02/10/2014 01:33 PM, Jeffrey Schnick wrote:

[300 words snipped]

I am open to change, but at present, I would call that atomic-level
energy that the object had, but later got radiated away, "thermal
energy".

Whenever I say there is no such thing as thermal energy, I try to be careful to
add the proviso: "except in trivial cases".

In particular, if the situation is so cramped that you can define a notion of
"thermal energy" aka "heat content", then it is so cramped that you could
not possibly build a heat engine.

You certainly can construct such situations ... but they are trivial.

In particular, subject to modest restrictions we can write the useful equation

dE = - P dV + T dS [1]

*If* you cobble up a situation where the P dV term is guaranteed to be zero,
*then* we can say two things:

A) The "heat" term i.e. T dS is the gradient of a potential.
You can integrate it and thereby /define/ a notion of
"heat content" aka "caloric" aka "thermal energy" as a
function of state.

B) This is a trivial victory, because in this situation, integrating
T dS is identical to integrating dE. In other words, the "thermal
energy" is just the /energy/ (to within a meaningless constant of
integration).

=========

I say again: You certainly can construct such situations. Indeed, such
situations are common and familiar. You don't need a water pistol in outer
space. If you warm up a baby bottle and then let it cool down, there is no P
dV term. The T dS term tells the whole story. Then:
A) In the short run, in this narrow situation, you have not much
to lose by talking about the "thermal energy" aka "caloric" aka
"heat energy" in the baby bottle.
B) OTOH you would do at least as well to talk about the plain
old /energy/, in this situation and every other.

The advantage of talking about energy rather than "thermal energy" is that
when we expand the scope of discussion to include P dV terms, to include
heat engines, to include physics and chemistry and engineering and all that
stuff, we get to keep the notion of energy. In contrast, the notion of
"thermal energy" is dead on arrival.

To repeat: when heating and cooling baby bottles, the idea of "thermal
energy" is not wrong; it's just trivial. It confers no advantage over plain old
/energy/.

In contrast, the idea of /energy/ is a keeper. You've got nothing to lose and
much to gain by focusing attention on the energy.
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