Re: [Phys-l] heat +- impulse

[John Denker <jsd@av8n.com>]

On 11/03/2007 04:53 PM, I dangled the following quote:

>   «You can strengthen your insight into these concepts by now returning to
>   the discussion of impulse and change of momentum in Section 1.9.  Notice
>   that impulse, like quantity of heat transferred, is path dependent.  In order
>   to calculate an impulse, we must know how the force delivering the impulse
>   varied instant by instant (i.e., we must know the "path" of the force with
>   respect to the succession of clock readings).  If we have this information, we can
>   evaluate the impulse as an integral (i.e., an  area under a graph).  The situation
>   with respect to transfer of heat is exactly analogous:  Delivery of impulse
>   (which is /not/ a state variable) results in a change in the state variable called
>   "momentum."  Transfer of heat (which is /not/ a state variable) at constant
>   pressure results in a change of the state variable temperature.» 


Several days have passed, and nobody has taken the bait, so I might 
as well give my analysis of this passage.  Avert your eyes if you're 
still trying to puzzle it out.



IMHO, this passage has more errors than it has sentences.

    One of the central points that this section tries to make is actually 
valid, if you take it out of context, and re-interpret it in just the right 
way: It is true that in non-cramped thermodynamics, there is no path-independent 
value for ∫ TdS.

    Alas, this passage buries this fact under two layers of wrong physics, 
plus a few layers of bad pedagogy.
        * The definition of “path dependent” is deeply flawed; see below.
        * The analogy between impulse and heat is flawed; see below.
        * Even if the analogy were overhauled so as to make it correct, it 
would violate the pedagogical principle that learning proceeds from the known 
to the unknown. If students don’t know about thermodynamics, you can’t explain 
it to them in terms of non-conservative force fields (which they don’t know 
about, either).
        * This makes a mockery of the of principle of “idea before name”. The 
title of this section is «HEAT IS NOT A FUNCTION OF STATE». If you learn those 
words by rote, they may turn out to be correct, if you later learn a correct 
definition for the words. However, the /ideas/ that this passage attaches to 
these words are not correct.
        * It is questionable (both from a pedagogical and from a practical 
point of view) to emphasize what something is not. Even if the passage gave 
a consistent definition of “heat” and a correct definition of “path independent” 
(which it does not), saying that heat is not path independent should not 
be the goal; it is barely even a starting place. It would have been more 
constructive to explain that T dS is a state function, and to explain some 
of the things we can do with it.

    The passage does not correctly explain the relationship between TdS 
(which is a function of state) and ∫ TdS (which is not). This could have 
been explained using pictures, such as the picture of uncramped thermodynamics 
in 
  http://www.av8n.com/physics/thermo-laws.htm
and also
  http://www.av8n.com/physics/thermo-forms.htm

    The definition of “path dependent” given here is wrong. The key question is 
not asked, let alone answered. The question is, what would happen if we chose a 
different path from state A to state B? The passage imparts quite a serious 
misconception about what path-dependent means.

It is always possible, but meaningless, to find a seemingly-path-dependent way 
of calculating a path-independent quantity.

    The statement about impulse might have been correct if it had considered 
paths through position-space instead of state-space. In particular, paths 
through the position-space inside a betatron can produce a path-dependent 
impulse, since momentum is not a function of position there, as discussed 
in 
  http://www.av8n.com/physics/non-conservative.htm

    However, the quoted passage is clearly talking about paths in state-space. 
That changes everything, because momentum is a function of state ... not a 
function of position per se, but a function of state. That allows us to carry 
out the following calculation:

    impulse = ∫	F dt             along some path from state A to state B   
            = ∫	(dp/dt) dt      
    	    = ∫	 dp   
            =  p(B) − p(A)       independent of path in state-space


    Also, introducing the term «delivery of impulse» violates the principle 
of “idea before name”. If this term means anything, it presumably is the same 
as transfer of momentum.

    Saying that impulse is path-dependent is tantamount to saying that the 
force field is non-grady. As a pedagogical point, just telling students that 
such a field exists is next to pointless. Students have a strong tendency to 
assume that every force field is the gradient of some potential. If you want 
’em to believe in (let alone understand) non-grady force fields, it will take 
some serious work, not just a sentence or two here and there.  The analogy 
here to “some” force field is neither concrete nor correct.  Diagrams would 
have been a big help.

    It says «Transfer of heat (which is not a state variable) at constant 
pressure results in a change of the state variable temperature.» I assume 
this is meant to be a general rule, since is not restricted to any particular 
scenario, and no limits to the validity of this statement are given.  This 
rule is inconsistent with basic physics in this context; it is simply not 
true that heat transfers of the kind considered in this paragraph always 
result in a change of temperature.

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

Is it any wonder that students come away confused about basic thermodynamics?