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Excuse my poor English, I have a lot to learn.

If all the particles of a gas had the same speed, the same direction, did not collide and were not subject to any external force, would the gas have a temperature, despite the fact that the particles would have an average kinetic energy ?

And what if all the particles had the same speed, were not subject to an external force but had random directions? Does the gas have a temperature?

If a gas A (10000 particles) had 1000 times more particles than a gas B (10 particles) and the particles of each gas had the same average kinetic energy, would the two gases have the same temperature ?

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If all the particles of a gas had the same speed, the same direction, did not collide and were not subject to any external force, would the gas have a temperature,

What you are describing is the kinetic energy of a container of particles as a whole with respect to an external frame of reference, i.e., the macroscopic kinetic energy of the container of gas.

However, in addition to the collective motion and kinetic energy of the gas, there is also always the kinetic energy associated with the random motion of the gas particles with respect to the center of mass of the container of gas. The temperature of the gas is based on the average kinetic energy of the those molecules, not the collective kinetic energy of the container of molecules as a whole.

And what if all the particles had the same speed, were not subject to an external force but had random directions? Does the gas have a temperature?

But the random speed of the particles of a gas cannot have the same speed. they follow the Boltzmann distribution. Only the collective motion of the particles can have the same speed, and that collective motion does not influence the temperature of the gas.

If a gas A (10000 particles) had 1000 times more particles than a gas B (10 particles) and the particles of each gas had the same average kinetic energy, would the two gases have the same temperature ?

Yes.

But they would not have the same total internal energy. For an ideal gas, where the internal energy consists only of kinetic energy, gas A would have 1000 times more internal energy than gas B.

Hope this helps.

Bob D
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  • HDE (https://physics.stackexchange.com/users/1916/hde), Temperature of a gas (assumptions about the particle speeds), URL (version: 2012-10-24): https://physics.stackexchange.com/q/41608 –  Nov 11 '22 at 02:57
  • Emilio Pisanty (https://physics.stackexchange.com/users/8563/emilio-pisanty), Temperature of a gas (assumptions about the particle speeds), URL (version: 2012-10-25): https://physics.stackexchange.com/q/41614 –  Nov 11 '22 at 02:58
  • It's a thought experiment. –  Nov 11 '22 at 02:58
  • @Priscilla Here’s a thought experiment for you. Suppose a person has a cup of coffee standing on the road. Do you think the temperature of that same cup of coffee would be higher if were in a car moving at constant speed with respect to the road? – Bob D Nov 11 '22 at 03:12
  • and then the temperature is more than an average kinetic energy. –  Nov 11 '22 at 03:19
  • as Emilio Pisanty seems to mean, right? –  Nov 11 '22 at 03:20
  • I’m afraid I don’t know what you’re talking about – Bob D Nov 11 '22 at 03:23
  • « I think the simplest response is to say that temperature is not a measure of the average kinetic energy of the gas particles, but rather to the spread of velocities from the mean value. If this spread is zero - as in your example of all the gas particles moving in the same direction - then the temperature is also zero. » Emilio Pisanty –  Nov 11 '22 at 04:00
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If all the particles of a gas had the same speed, the same direction, did not collide and were not subject to any external force, would the gas have a temperature, despite the fact that the particles would have an average kinetic energy ?

The kinetic definition of temperature is given in the rest frame of the bulk of matter consisting the gas.

kin

kinetic

It would not be a gas, and it would not have a temperature.The rest frame of your hypothesis has all the gas molecules at rest by definition.

And what if all the particles had the same speed, were not subject to an external force but had random directions? Does the gas have a temperature?

Yes, in the center of mass rest frame of the system there would be a temperature.

If a gas A (10000 particles) had 1000 times more particles than a gas B (10 particles) and the particles of each gas had the same average kinetic energy, would the two gases have the same temperature ?

If in the rest frame of the group,yes, by definition.

anna v
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The short answer is that energy is not frame-invariant. Thermodynamics and, as a consequence Statistical Mechanics at equilibrium, assume that all the energies are measured in a reference frame where the center of mass of the system is at rest.

Therefore, independently of its speed, an ice cube keeps always the same temperature.

GiorgioP-DoomsdayClockIsAt-90
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  • Thank you for your answer! Could you please take a look at my other question about sel-gravitating molecular gas clouds?

    Priscilla (https://physics.stackexchange.com/users/349993/priscilla), What would be a good particle point-of-view model of a self-gravitating molecular cloud: with orbit or not?, URL (version: 2022-11-11): https://physics.stackexchange.com/q/735760

     –  Nov 11 '22 at 21:55