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When talking about liquids or gases they are both a measure of the kinetic energy of a collection of molecules. And in devices like jet engines temperature is converted directly into velocity. So, why isn't something hot when it picks up velocity? And why doesn't something move when it gets really hot?

My main question is is the only difference between temperature and velocity the direction the volume moves?

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    $\begingroup$ temperature of an ideal gas is proportional to the statistical variance of the velocity of the molecules while the gross kinetic energy is proportional to the square of the average velocity of the molecules. $\endgroup$ – hyportnex Nov 24 '16 at 19:04
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The average random molecular velocity (whose direction is, in a stochastic sense, evenly distributed in space and whose direction changes constantly through collisions) corresponds to temperature in e.g. kinetic gas theory. This has nothing to do with the macroscopic velocity which has a direction. So yes, the difference between the velocity that can be associated with temperature and the macroscopic velocity we talk about in fluid/continuum mechanics is the randomness or non-randomness of their direction. Which is a very important distinction, though.
This means that something does not move when it gets really hot because the displacement the velocity due to thermal motion is on the average zero. The thermal velocity that can be assigned to every molecule/atome changes its direction constantly through collisions with other molecules/atoms.
For the same reason, something does not get hot when it is moving - because the random velocity of the single particles does not change.


As has been pointed out in the comments, it might be worth to also mention the scale seperation of those velocities. To quote Pirx from the comments:

As an aside, the average molecular velocity in an ideal gas is of the order of the speed of sound in that gas. Thus, for practical, every-day situations, the velocity of the gas molecules is much, much higher than the macroscopic velocity of the gas flow.

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  • $\begingroup$ As an aside, the average molecular velocity in an ideal gas is of the order of the speed of sound in that gas. Thus, for practical, every-day situations, the velocity of the gas molecules is much, much higher than the macroscopic velocity of the gas flow. $\endgroup$ – Pirx Nov 24 '16 at 15:46
  • $\begingroup$ @Pirx that's a nice aside - do you mind that I edited a quote of it into the answer? $\endgroup$ – Sanya Nov 24 '16 at 15:50
  • $\begingroup$ Not at all, go right ahead! $\endgroup$ – Pirx Nov 24 '16 at 15:51
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It is a popular belief that temperature is actually the average kinetic energy of molecules/atoms (up to a factor). However, this is only true in classical mechanics (although one should have in mind the points about random and macroscopic velocities made by Sanya in another answer). However, this is not true in quantum mechanics. For example, the average kinetic energy in an ideal Fermi gas is high at absolute zero. Therefore, the average kinetic energy of electrons in solids is pretty much unrelated to the temperature at room temperature and below (as the room temperature is much lower than the Fermi energy (in natural units)).

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  • $\begingroup$ Could you perhaps elaborate on this. Is it wrong then to say macroscopic sensations of temperature are interpretations of avg. ke? Like when I feel something is hot is it avg. KE or some phenomenon that can only be described at the quantum level? $\endgroup$ – BoddTaxter Nov 25 '16 at 10:20
  • $\begingroup$ @BoddTaxter: First off, it is not clear to me what macroscopic sensations of temperature are. For example, metal at 20C feels colder than wood at the same temperature, as their thermal conductivities are different. If, however, we decide that the heat you lose or gain between the moment you established a thermal contact with a small body and the moment this body acquires the temperature of your body is a measure of the sensation of temperature, then yes, typically it's the average kinetic energy that you feel, but not always and not exactly, (cont.) $\endgroup$ – akhmeteli Nov 25 '16 at 15:09
  • $\begingroup$ @BoddTaxter: as, while, say, heat capacity of most materials at room temperature is correctly described by a classical law (Dulong-Petit law), this is wrong for some materials, such as diamond, where deviation from the law due to quantum effects is very large. $\endgroup$ – akhmeteli Nov 25 '16 at 15:12

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