Consequently the likelihood at any instant of finding a particle at any given position in the container is the same as at any other position or instant -- there is no "preferred" position for the particles.
Alas, that's not right. Consider for example a column of air several miles high. Any particular molecule is more likely to be found near the bottom than near the top. Also the relative concentration will change as a function of altitude, with heavier molecules being more prevalent near the bottom.
As indicate in table 19.1 on page 508, the reasoning in section 19.3 runs parallel to the reasoning in section 19.2. This is supposed to make each of them more plausible, but in fact they are equally fallacious.
Thermodynamics does have a notion of "spreading" ... but it is the spreading of probability in an abstract high-dimensional space. It is absolutely not the spreading of particles per unit space, energy per unit space, or energy per unit particle.
See item #155 for a catalog of entropy-related issues.
On page 507 the key passage in section 19.3 says
Alas, that's not right. Consider for example a column of air several miles high. Any particular molecule is more likely to be found near the bottom than near the top. Also the relative concentration will change as a function of altitude, with heavier molecules being more prevalent near the bottom.
As indicate in table 19.1 on page 508, the reasoning in section 19.3 runs parallel to the reasoning in section 19.2. This is supposed to make each of them more plausible, but in fact they are equally fallacious.
Thermodynamics does have a notion of "spreading" ... but it is the spreading of probability in an abstract high-dimensional space. It is absolutely not the spreading of particles per unit space, energy per unit space, or energy per unit particle.
See item #155 for a catalog of entropy-related issues.