In considering this putative violation of conservation rules,
This is not a violation of conservation rules, Brian - rather, it is a
confirmation of them. Just one of the numerous cases in which heat is (or can be)
converted into work. Due to the second law, however, these cases are neither
taught nor learned. Even thinking about them is forbidden. I remember a Danish
biophysicist telling me that, whenever he wanted to tease his colleagues, he
simply asked them: "At the expense of what energy does the electrochemical cell
Zn2+ (high concentration), Zn II Zn, Zn2+ (low concentration)
do work?" His colleagues got confused but nobody ever dared even to think of
environmental heat as a possible source of energy.
For the same reason, it is impossible to teach an extremely clear and useful
interpretation of the osmotic pressure. According to this interpretation, osmotic
pressure is analogous and in a sense even identical to gas pressure. But if so,
osmotic pressure, like gas pressure, must be able to convert environmental heat
into work - a forbidden topic. So students are forced to learn that the osmotic
pressure is due to "the tendency of the solvent to flow from a high to a low
chemical potential". Neither teachers nor students have any idea of the physical
meaning of this statement. They just learn it by rote and tranfer it from
generation to generation.