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Tyrrell_McAllister comments on Entropy and Temperature - Less Wrong
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This is a good article making a valuable point. But this —
— is a confusing way to speak. There is such a thing as "the average kinetic energy of the particles", and one measure of this thing is called "temperature" in some contexts. There is nothing wrong with this as long as you are clear about what context you are in.
If you fall into the sun, your atoms will be strewn far and wide, and it won't be because of something "in the mind". There is a long and perfectly valid convention of calling the relevant feature of the sun its "temperature".
An alternate phrasing (which I think makes it clearer) would be: "the distinction between mechanical and thermal energy is in the mind, and because we associate temperature with thermal but not mechanical energy, it follows that two observers of the same system can interpret it as having two different temperatures without inconsistency."
In other words, if you fall into the sun, your atoms will be strewn far and wide, yes, but your atoms will be equally strewn far and wide if you fall into an ice-cold mechanical woodchipper. The distinction between the types of energy used for the scattering process is what is subjective.
The high-school definition of temperature as "a measure of the average kinetic energy of the particles" (see the grandparent comment) actually erases that distinction as it defines temperature through kinetic (mechanical) energy.
I didn't read your comment carefully enough. Yes, we agree.
Right, but we don't think of a tennis ball falling in a vacuum as gaining thermal energy or rising in temperature. It is "only" gaining mechanical kinetic energy; a high school student would say that "this is not a thermal energy problem," even though the ball does have an average kinetic energy (kinetic energy, divided by 1 ball). But if temperature of something that we do think of as hot is just average kinetic energy, then there is a sense in which the entire universe is "not a thermal energy problem."
That's because temperature is a characteristic of a multi-particle system. One single particle has energy, a large set of many particles has temperature.
And still speaking of high-school physics, conversion between thermal and kinetic energy is trivially easy and happens all the time around us.
A tennis ball is a multi-particle system; however, all of the particles are accelerating more or less in unison while the ball free-falls. Nonetheless, it isn't usually considered to be increasing in temperature, because the entropy isn't increasing much as it falls.
I think more precisely, there is such a thing as "the average kinetic energy of the particles", and this agrees with the more general definition of temperature "1 / (derivative of entropy with respect to energy)" in very specific contexts.
That there is a more general definition of temperature which is always true is worth emphasizing.
Rather than 'in very specific contexts' I would say 'in any normal context'. Just because it's not universal doesn't mean it's not the overwhelmingly common case.