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I am tempted to wonder if you understand what 'calorimetry' means, atthe
least in the way Ludwik and many others are using it. 'Calorimetry' is
measurement of changes in internal energy, usually* by the means of
measuring the temperature change of a object with known heat capacity
(as in a 'bomb calorimeter'). In its modern usage, 'calorimetry' has
*nothing* to do with 'caloric' the non-existant substance (except
etymologically).
Now, to do Joule's paddle wheel experiment, you need to measure the
work done, measure the change in internal energy, and compare them. The
second step *is* calorimetry. I don't see any way around that.