# [ExI] The subjectivity of entropy, the role of the observer...==> Rational metaethics

Lazy Dragon laziestdragon at gmail.com
Fri Feb 29 16:23:51 UTC 2008

```On Fri, Feb 29, 2008 at 10:23 AM, Eliezer Yudkowsky <sentience at pobox.com>
wrote:

> On Thu, Feb 28, 2008 at 8:54 PM, Lee Corbin <lcorbin at rawbw.com> wrote:
> >
> >  Almost all the time, I stick with this idea:  Temperature of a
> >  gas is the mean kinetic energy of its molecules.
>
> Aren't there vibrational degrees of freedom that also contribute to
> kinetic energy, and isn't that why different materials have different
> specific heats? I.e., what matters is kinetic energy per degree of
> freedom, not kinetic energy per molecule? So you actually do have to
> think about a molecule (not just measure its kinetic energy per se) to
> determine what its temperature is (which direction heat will flow in,
> compared to another material), even if you know the total amount of
> heat - putting the same amount of heat into a kilo of water or a kilo
> of iron will yield different "temperatures".
>
> But the more important point: Suppose you've got an iron flywheel
> that's spinning very rapidly. That's definitely kinetic energy, so the
> average kinetic energy per molecule is high. Is it heat? That
> particular kinetic energy, of a spinning flywheel, doesn't look to you
> like heat, because you know how to extract most of it as useful work,
> and leave behind something colder (that is, with less mean kinetic
> energy per degree of freedom).
>
> If you know the positions and speeds of all the elements in a system,
> their motion stops looking like heat, and starts looking like a
> spinning flywheel - usable kinetic energy that can be extracted right
> out.
>

Actually, I'm fairly certain that  a spinning flywheel's kinetic energy to
be contributes to its temperature.  If chill a flywheel to 1 degree Kelvin,
spin it up very fast, and then place it in a bath of liquid Helium you'll
find that energy will flow from the flywheel to the surrounding bath rather
than vice versa.  Since heat transfer is always from the hot object to the
cold object and since temperature is defined in terms of heat transfer this
means that the spinning flywheel is really hotter than the stationary
flywheel.  However, because the amount that kinetic energy contributes to
the temperature of an object is normally such a tiny proportion of its
thermal energy we typically neglect it when doing calculations.

Also, since even though temperature and heat aren't exactly the same thing
we can say that temperature always increases as thermal energy increases.
Since thermal energy is defined as the sum of the every particle's kinetic
energy the fact that the momentums of all the different particles line up or
are known doesn't have any effect on thermal energy.  If increasing the
velocity of an object increases its thermal energy, it must be that it also
increases its temperature.  If knowing the state of every atom in an object
does not decrease its thermal energy, it cannot decrease its temperature.
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