Just a thought that came to mind ...

The rockets on interplanetary scouts fire to impart motive/braking force to the craft. This force, I understand, is simply a reaction engine - the exhaust departs out the nozzle, and drives the engine & attached craft in the desired direction. In an atmosphere this exhaust would eventually disperse. In space one would expect the exhaust to continue in the direction it exited the nozzle. But space is cold.

Assuming the rockets fired in space far enough for any gravity knot to have negligible effect, how far from the nozzle would the exhaust cool to near CBR temperature?

For instance, the hydrazine thrusters on the Voyagers provided necessary motive force at critical times during it's transit through Our solar system... albeit this was necessarily within a gravity knot.

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    $\begingroup$ Now that Space.SE has become a public beta, this question is a nice fit there. But, I don't say this is off-topic here too ;-) $\endgroup$ – Waffle's Crazy Peanut Jul 24 '13 at 1:58

In space the exhaust gases will never cool. They will get more and more diffuse, but the temperature will remain the same.

We measure the temperature of a gas by measuring the speed profile of the particles (molecules, atoms or whatever) and comparing the measured speed profile with the Maxwell-Boltzmann distribution. In an atmosphere the particles in the exhaust gas will collide with air molecules and transfer energy to them, and the energy of the exhaust gas particles will eventually settle down to match the energy, and therefore the temperature, of the air molecules. In a vacuum the exhaust gas molecules will just carry on going. Their speed won't change and therefore neither will their temperature.

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    $\begingroup$ Now I'm really confused, and I feel really daft asking this, but what about radiation? The gas will radiate, surely, unless it encounters and absorbs radiation? I admit I haven't done any calculations, but if I'm right I'm guessing it must be really slow. $\endgroup$ – WetSavannaAnimal Jul 24 '13 at 10:26
  • $\begingroup$ Gas molecules don't radiate on their own. They radiate when they collide with other gas molecules and generate the temporary dipoles that emit the EM radiation. The exhaust from a rocket engine is more like a molecular beam and collisions between molecules are going to be rare. $\endgroup$ – John Rennie Jul 24 '13 at 11:07
  • $\begingroup$ Got it! Thanks. It actually becomes apparent as soon as you sit down to try to do a calculation - your thoughts go "Stefan Boltzmann law ... no wait, that's for radiation itself... how does radiation get into equilibrium with the matter? ... where does it even come from? ... wait these guys are moving at constant velocities ... " from there there's only one conclusion, that they radiate when they accelerate during a collision! The molecular beam analogy's a good one, but even a hot bubble will be the same since the mean free path will swiftly lengthen and shut off collisions. $\endgroup$ – WetSavannaAnimal Jul 24 '13 at 11:44

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