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There is a work-energy theorem by means of which the two quantities may
be seen to be related, much as the height of a water column is related
to the pressure at its base. Height and pressure are not the same thing,
however, even if the latter is expressed in the units of the former,
a [still] common practice.
........ two quotation from Hans U. Fuchs (A.J.P. March 1987).
The article refers to the innovative German way of teaching energy at
the introductory level.
1) In 1970s, Falk et al. came up with a concept of teaching physics based
on "substancelike" quantities ... as the carriers of energy in physical
processes. Entropy is the carrier of energy in thermal phenomena. This
is a very simple picture which helps us to .....
2) Clausius gave the name of "entropy" and defined it as an integral of
dQ/T. Such a definition appeals to a mathematician only. In justice
to Carnot, it should be called caloric, and be defined directly from
his equation W = A*Q*(T-To), which any schoolboy could understand.
[Here, W is the work done by a quantity Q of caloric falling from a
temperature T to To; A is a convestion factor ...].
The second quotation is itself a quote from a 1911 paper. Schoolboys were
very knowledgable in those days. As you probably know, Carnot's model of
a heat engine was a water wheel. This explains the terminology of
"falling" from one temperature to another.
Note that in SI A would be equal to 1 and the unit of Q would be J/K, as
for entropy. Interesting! But do we really want to resurect caloric and
give it a new interpretation? I am not automatically agains this. But I
want to hear good arguments favoring this approach. Why is it better than
what has been developed since then. [A conservative approach based on
"If it ain't broke don't fix it".]