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For an ideal gas, we can relate temperature to the average kinetic energy of the gas molecules.

What if we view a container of this gas from a reference frame that is translating at constant speed relative to the container.

$$E[X^{2}] = Var[X] + E[X]^{2}$$

The distribution of speeds is the same, but since the mean is larger (it is zero in the rest frame of the container), then the observer would view a higher average kinetic energy. Does the moving observer say that the container of gas is hotter?

If bulk translation doesn't relate to temperature, is there some hidden zeroing that's not present in the simple statement of "average kinetic energy"?


marked as duplicate by user197851, Community Apr 9 at 11:44

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  • $\begingroup$ @Gert No, the squares are in different places. That is the distribution of speeds in the same, but the expected squared value is greater because the mean is greater. $\endgroup$ – Zhe Apr 8 at 22:35
  • $\begingroup$ Oooopsie, my bad. Must learn to read one day. $\endgroup$ – Gert Apr 8 at 22:38
  • $\begingroup$ Also related: physics.stackexchange.com/questions/186655/…. $\endgroup$ – user197851 Apr 9 at 9:58