[Phys-L] thermo : instructional sequencing

[John Denker <jsd@av8n.com>]

Context:  we are talking about a physics course where calculus is a 
co-requisite, not a pre-requisite.

On 06/10/2013 03:58 PM, Bruce Sherwood wrote:

> there is
> a general desire on the part of instructors to have in a textbook a bit
> more than can typically be treated, to provide at least in theory some
> flexibility in what to do            [1]

Sure.  That is entirely reasonable.

Note that in some well-crafted books, each chapter tells you to what
extent later chapters depend on it.  That way you can figure out what 
you can skip and what you can't ... and also tells you to what extent
you can re-arrange the sequencing.

Another argument that leads to the same conclusion is that students
are *supposed* to take responsibility for their own education.  Some
of them will keep their books, and will eventually learn the stuff
in the book, even if it wasn't covered sufficiently (or at all) in
class.  Consider the following conversation:
 me:       How much do you know about such-and-such?
 student:  We didn't cover that in class.
 me:       I didn't ask whether it was covered in class.  I
           asked how much you knew about it.  You need to take
           responsibility for learning stuff, including stuff
           that isn't covered in class.  There isn't time to
           cover more than about 10% of the stuff you need to know.

As for thermo in particular, I remember being "exposed" to it as
a freshman.  However, I did not understand it -- not the slightest
clue -- until many years later.

>  almost no one gets to Chapter 13,
> in which there is the discussion of heat engines, including nonzero-power
> heat engines. Even in an honors course at Carnegie Mellon, with very
> strong, well-prepared students, we didn't get to heat engines.    [2]
 
That makes a certain amount of sense.

By way of analogy:
 ++ Riding a bicycle to the corner store is fairly easy, provided you 
  already have a bicycle and know how to ride it.
 -- If you've never ridden before, it's going to take you a while to 
  learn the technique.

So it is with thermo.  Any thermodynamics worthy of the name -- i.e.
anything that analyzes heat engines -- depends on a few critical
concepts, including probability as well as multivariate calculus.
 *) The students were not born knowing these things.
 *) The typical first-year calculus course says very little about
  probability ... and possibly nothing at all.  The math professor
  is just as pressed for time as the physics professor (see item 
  [1] above).  He might decide to soft-pedal the probability stuff,
  assuming it was ever on the syllabus to begin with.  
 *) The typical first-year calculus course probably doesn't touch
  multivariate calculus at all.

There are eleventeen good reasons why it would be nice to cover heat
engines in the first-year physics course ... but as the philosopher
Jagger observed, you can't always get what you want.

Even in a junior-level semester-long course devoted entirely to 
thermo, where probability and multivariate calculus are prerequisites, 
you spend most of the time upgrading the students' math skills.
That's because the way the two critical topics are covered in the 
typical Calculus-III course is too shoddy as to serve as a basis 
for doing thermo.  For example, the conventional notation for
partial derivatives is begging to be misinterpreted.  Similarly, 
the conventional notation for conditional probability is begging 
to be misinterpreted.

Many widely-used thermo books are full of equations that violate
basic mathematical principles ... Schroeder being a notable exception.

To make this specific and concrete: Suppose you want the student to
understand that:
 -- T dS is a vector in some abstract high-dimensional space
 -- T dS is not the gradient of any potential

Most students have no clue what that means.  On the other hand, 
if/when they get to the point where they understand that, thermo 
gets a *lot* easier.

Also, as a specific suggestion:  I recommend not going anywhere 
near heat engines until the students have seen AC electromagnetic
fields and AC circuits.  This lays down some crucial foundation,
because
  -- the E field in a betatron is a vector
  -- the E field in a betatron is not the gradient of any potential

Additional discussion of this, including some helpful diagrams, can
be found at
  http://www.av8n.com/physics/non-grady.htm

Also, as mentioned in the other thread this morning, for an introduction
to probability from a modern (post 1933) viewpoint, see
  http://www.av8n.com/physics/probability-intro.htm

For thermo in general, with "most" of the completely-wrong stuff
excluded, see
  http://www.av8n.com/physics/thermo/