![]() ![]() If liquid water at 273 K, with its 10 1,991,000,000,000,000,000,000,000 accessible microstates (quantized molelcular arrangements) is considered "disorderly", how can ice at 273 K that has 10 1,299,000,000,000,000,000,000,000 accessible microstates be considered "orderly"? Obviously, using such common words is inappropriate in measuring energetic microstates and thus in discussing entropy change conceptually. The common older textbook comparison of orderly crystalline ice to disorderly liquid water is totally deceptive, It is a visual "Boltzmann error" not a proper thermodynamic evaluation. Thus, today we know that no system above 0 K has any "order" in correct thermodynamic descriptions of systems of energetic molecules. When this is the case, then whenever two of more small parts of it come into interaction with each other, the system formed by these parts is also initially in an ordered state and when left to itself it rapidly proceeds to the disordered most probable state.” (Final paragraph of #87, p. “In order to explain the fact that the calculations based on this assumption correspond to actually observable processes, one must assume that an enormously complicated mechanical system represents a good picture of the world, and that all or at least most of the parts of it surrounding us are initially in a very ordered - and therefore very improbable - state. I have inserted an explanatory clause from the preceding paragraph in brackets, and put in italics Boltzmann’s surprisingly naïve assumptions about all or most initial states as “ordered”.) (The preceding and following phrases and sentences, disappointingly, only expand on it or support it without additional meaningful technical details or indications of Boltzmann’s thought processes. The key paragraph should be quoted in full. The important question is “what are the bases for Boltzmann’s introduction of order to disorder as a key to understanding spontaneous entropy change?” That 1898 idea came from two to three pages of a conceptual description, a common language summary, that follow over 400 pages of detailed theory in Brush’s translation of Boltzmann’s 1896-1898 “Lectures on Gas Theory” (University of California Press, 1964). Planck’s nobility in allowing R/N to be called ‘Boltzmann’s constant’, k B, was uncharacteristic of most scientists of that day, as well as now. ![]() LnW \), and subsequently carved on Boltzmann’s tombstone. ![]()
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