Re: [Phys-L] heat content

[John Denker <jsd@av8n.com>]

On 02/12/2014 04:20 PM, Chuck Britton wrote:
> Could we say something like 
>
> “The temperatures of the oceans have increased by a certain amount, on average.” 
>
> Would that be understandable without being too ‘incorrect’.

That's entirely correct and non-misleading as far as it goes.

OTOH the article that provoked this discussion was talking about
energy, so if we want to answer the original question we need
to convert temperature to energy.

Temperature is well defined and energy is well defined, but they
are not the same thing.  Really not.

We can convert one to the other in various ways.  In the present
context, we can use the heat capacity.  That's another well-defined
thing.  The heat capacity of the ocean is eeeeenormous.

This is exactly where the average person's thinking about thermodynamics
goes off the rails.  They define a Q-function such that ΔQ = C ΔT and
everything *appears* to work ... in context.  It works for cramped 
thermodynamics, i.e. for situations so limited that you cannot build
a heat engine.

When you extrapolate to real thermodynamics, you get to keep the
ideas of energy, temperature, heat capacity, and lots of other
things, but you do *not* get to keep the Q-function.  

So what the original article did was not wrong;  it's just brittle
and risky.  They can get away with it /in context/ but it does
not generalize to other contexts.

There are good physics reasons why they can get away with "heat
content" in context.  There are also good physics reasons why it 
doesn't generalize.  Changing the terminology will not solve
this part of the problem.  I mention this so as to remind people 
that demanding the article authors say "thermal energy" rather 
than "heat energy" is no improvement whatsoever.

==============================

On 02/12/2014 03:45 PM, I wrote:

>  The thesaurus lists "distributed" as an antonym for collective,
>  but that's guaranteed to convey the wrong idea, because 

The gremlins ate the rest of my paragraph.  What I meant to say
was:

 The thesaurus lists "distributed" as an antonym for collective,
 but that's guaranteed to convey the wrong idea, because 
  a) The rabble modes are scattered, not evenly distributed, and
  b) Commonly both the collective modes and the rabble modes 
   fill all of space;  the rabble modes are more spread out in
   some abstract /phase space/ not ordinary position-space.

Also:

> -- All of this is a sideshow, because it doesn't cover the
>  general case.  There remain lots of situations where we
>  simply must divide the system in to parcels, into subsystems,
>  and there is no reason to expect that there will be anything
>  resembling a "thermal" / "non-thermal" distinction.  Examples
>  include:
>    NMR spin/lattice distinction
>    Styrofoam box containing a hot potato and a cold potato
>    Brownian motion
>    etc. etc. etc.

Add to that list fluid dynamics, including hydro-dynamics and
even -statics.  You have to divide the fluid into parcels or
you'll never get anywhere.

=====================

I've been thinking about the pedagogical angles.  It's a mess.
At the moment, I'm of the opinion that the styrofoam box with
two potatoes makes a good starting point.  It's a system
with two subsystems.  There's nothing tricky about it, if you
think about it in the right way ... OTOH most people don't
think about it the right way ... but I'm working on it.  I'm
trying to cook up some words and diagrams to make this easier
to understand and easier to explain.  Watch this space.