Joel, you were basically right. I did have in mind a hydrocarbon and
oxygen in a combustion process producing carbon dioxide and water.
So the mole numbers change as a result of the process. Unfortunately,
I was thinking in terms of an isothermal process even though it was
clearly adiabatic, and so it led me to the error of saying that dU ~= 0.
But my point still holds, which is that there is no such thing as
thermal energy, and in the example of combustion it is necessary to
consider U as a function of mole numbers. What actually happens from
the point of view of classical thermodynamics is that as the mole
numbers change, without the internal energy changing, it is necessary for
the temperature to change, and this change has nothing to do with heat,
which is in fact zero. A change in temperature does not require that
heat has been transfered. And sometimes heat is tranfered and there is
no change in temperature such as with changes in phase.