The Lorenzian Waterwheel
Most casual armchair scientists have no access to uniformly smooth boxes and elemental gases, much less instruments to measure the speed of the moving gases.
A metaphor for the gas chamber is found in the Lorenzian waterwheel. This is a thought experiment. Imagine a waterwheel, with a set number of buckets, usually more than seven, spaced equally around its rim. The buckets are mounted on swivels, much like Ferris-wheel seats, so that the buckets will always open upwards. At the bottom of each bucket is a small hole. The entire waterwheel system is than mounted under a waterspout.
Begin pouring water from the waterspout. At low speeds, the water will trickle into the top bucket, and immediately trickle out through the hole in the bottom. Nothing happens. Increase the flow a bit, however, and the waterwheel will begin to revolve as the buckets fill up faster than they can empty. The heavier buckets containing more water let water out as they descend, and when the water is gone, the now-light buckets ascend on the other side, ultimately, to be refilled. The system is in a steady state; the wheel will, like a waterwheel mounted on a stream and hooked to grindstone, continue to spin at a fairly constant rate. But even this simple system, sans boxes or heated gases, exhibits chaotic motion. Increase the flow of water, and strange things will happen. The waterwheel will revolve in one direction as before, and then suddenly jerk about and revolve in the other direction. The conditions of the buckets filling and emptying will no longer be so synchronous as to facilitate just simple rotation; chaos has taken over. The explanation for the irregular movement of the gas lies at the molecular level. While the box sides may seem smooth and thus the flow of the should always be regular, at molecular levels the sides of the box are quite irregular due to the motion of atoms and molecules. After all, in any solid not at absolute zero, total entropy is positive and there must be some irregularity in the molecular structure of the sides of the box. Molecular interactions are tiny, however. How would such tiny things like slightly misplaced molecules affect the flow of the gas in such a profound way as to cause seemingly random motion? The theory behind how small deviations can lead to large deviations lies at the heart of chaos theory. The explanation is simple, and in retrospect, obvious explanation commonly known as sensitive dependence on initial conditions.
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