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SilasBarta comments on The Second Law of Thermodynamics, and Engines of Cognition - Less Wrong
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Comments (65)
For a gas in a mass-sealed container, average vx, vy, vz are also zero, just as in the shaft, so this trivially matches.
You're correct that I should have said speeds, and I should have mentioned that the shaft requires a special shape/density distribution, but the point stands: The molecular property distribution doesn't by itself tell you how cold something is, or how much energy can be extracted -- it's also relevant how its degrees of freedom are constrained, which shows how your knowledge of (mutual information with) the system matters.
Yes, but the average tells you little that's meaningful: it's equivalent to the overall velocity of the gas as whole.
I agree with your overall point. Temperature is not directly a property of the system, but of how we can characterize it, including what constraints there are on it. I just think that this wasn't a great example for that point of view, precisely because you claimed agreement of distributions that doesn't exist.
A better way to say explain this can use the shaft. A shaft has the very strong constraint that position and velocity are perfectly correlated. This constraint lets us extract virtually all the kinetic energy out. A gas that had the same distribution of velocities, but lacked this constraint, would be very hard to extract useful energy from. No simple arrangement could do much better than treating it as a thermalized gas with the same average kinetic energy (and it would quickly evolve so that the velocity distribution would match this).
Sure it does -- it just requires a special shaft shaping/material. Hence the "a metal shaft could ..."
Otherwise, we're in agreement.
It's a really great point; thank you.