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I am an A-level physics student, and I've been taught that temperature is the average kinetic energy of a particle. So when gas particles are heated, they move faster. This makes sense as an airplane traveling faster does make the nearby air warmer when measured from the plane.

Say I release a box of room temperature atmospheric pressured gas in the vacuum of space. Assuming there is no gravity, all the gas particles will be traveling in a straight line as they won't be bumping into other particles. And since space is only a few degrees above absolute zero, the gas particles will cool down after they transferred a lot of their "thermal" energy via radiation, and thus should slow down (lower temperature = lower speed). Looking at a single gas particle this breaks the conservation of momentum, as it is quite literally slowing down to nothing. So what's going on.

Now imagine there is indeed gravity in space, the gas particles will eventually start traveling and be accelerated toward a source of gravity. So its kinetic energy increases and so does its temperature (higher speed = higher temperature). First of all it is heated up by nothing without any sort of heat transfer taking place, and would there be any distinction between temperature and speed? Why does this only seem to apply to gas and not solids - a fast moving car wouldn't look hotter would it (ignore friction with air).

So can anyone point out where the chain of logic breaks down because it is not making any sense.

John Rennie
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Siriusmart
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3 Answers3

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A single molecule does not have a temperature. This has been explored before in several questions. See this search for some examples.

For a system to have a temperature it needs to be in thermal equilibrium. This means it needs to have many degrees of freedom and to be efficiently exchanging energy between those degrees of freedom. For a monatomic ideal gas in a box the degrees of freedom are the momenta of all the atoms and the energy exchanging is done by collisions. None of this applies to a single atom travelling in a vacuum.

And since space is only a few degrees above absolute zero, the gas particles will cool down after they transferred a lot of their "thermal" energy via radiation, and thus should slow down (lower temperature = lower speed).

Single gas molecules don't slow down by radiating. Apart from anything else this wouldn't conserve momentum. Once your single molecule has escaped into space it remains at the same velocity (unless it collides with something).

You are quite correct that gas molecules falling into a gravitational potential well will accelerate but this doesn't change their temperature because single molecules don't have a temperature. If many gas molecules fall into a potential well, then come to equilibrium with each other, the temperature will have increased. That increase comes from their gravitational potential energy i.e. the GPE becomes more negative while their KE increases so their total energy hasn't changed.

John Rennie
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It appears you have two main misconceptions about temperature.

  1. Temperature is a macroscopic property of a collection of molecules. A single molecule doesn’t have a temperature.
  2. Temperature is a measure of the average kinetic energy associated with the random motion of the individual molecules, not the motion of the collection of molecules as a whole. Thus their collective speed with respect to an external reference frame, such as your gas molecules moving in a straight line in space, doesn’t affect the temperature of the collection of molecules.

Hope this helps.

Bob D
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Thermal radiation is kinetic energy becoming orbital energy that gets radiated away when electrons revert to their ground state, right? The electron in a hydrogen atom can't lose energy if it's in the ground state. Electrons won't leave the ground state if they are too far away to interact with other particles. I don't think the particles will lose energy when released into space, so won't slow down.

Nothing can ever slow down to $0$ in any absolute sense. Everything is always moving with respect to something else.

A fast moving car emitting thermal radiation would have waves blue shifted when coming towards you and red shifted when moving a way. Blue shifts in a static system tend to indicate higher temperature, so I think moving things would appear hotter when moving toward you and when failing to account for the doppler effect.

R. Romero
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