Cooling a gas by releasing it into vacuum: Entropy?

[greypilgrim]

Hi.

I just read an article where following cooling method is described. Apparently it's very common, but I don't know what it's called:

A gas under pressure is released into a vacuum through a small hole. The average particle speed in this beam of gas is the same as before, but the distribution is much narrower, and also all particles move in about the same direction. Although the energy didn't change, the temperature of the gas is much lower than before, because an observer flying next to the beam with the average particle speed would only see slowly moving particles.
In short, thermal energy has been converted into kinetic energy.

Now this seems a lot like the entropy of the gas decreased. The process looks irreversible though, so there surely must be a bigger entropy increase somewhere, but where? I suspect it's probably the increase in volume, but in the illustrations in the article the particle beam looks very narrow and the particles pretty localized.

 

[scottdave]

I'm not sure about how you would calculate it, but do you think you could heat up the stream of particles, and they would shoot back into the tiny hole in the container? The answer to this should give you some insight to what is happening with the entropy.
The following video has a pretty interesting explanation of how entropy works.

 

[jartsa]

Hi.
I suspect it's probably the increase in volume, but in the illustrations in the article the particle beam looks very narrow and the particles pretty localized.

Then there is an error.

Small hole: Particles fly in all directions.

A nozzle: Particle beam expands more slowly than in the previous case.

A very large nozzle: Particle beam expand very slowly after leaving the nozzle. Particle beam's thickness near the nozzle is about the same as nozzle's diameter.

 

[scottdave]

A beam of particles is not going to stay in a narrow beam unless something is forcing to stay in that beam - a pipe for example. Otherwise, when particles bang into each other, some will bounce in a different direction than the main beam, causing the group of particles to spread.

 

[jartsa]

A beam of particles is not going to stay in a narrow beam unless something is forcing to stay in that beam - a pipe for example. Otherwise, when particles bang into each other, some will bounce in a different direction than the main beam, causing the group of particles to spread.

Beams where particles collide behave the same way as beams where particles do not collide, because ... both beams are made of gas. Pressure of beam does not matter. Temperature matters.

 

[Andrew Mason]

A gas under pressure is released into a vacuum through a small hole. The average particle speed in this beam of gas is the same as before, but the distribution is much narrower, and also all particles move in about the same direction. Although the energy didn't change, the temperature of the gas is much lower than before, because an observer flying next to the beam with the average particle speed would only see slowly moving particles.
In short, thermal energy has been converted into kinetic energy.

Your example illustrates the principle behind the Bernoulli equation which is about conservation of energy. The pressure in the gas that passes into the vacuum drops to 0 and freely expands into the vacuum. After leaving the hole the gas molecules travel in all directions except backward (i.e over a 180 degree range) so the centre of mass of the expelled gas moves away from the hole at an average speed given by Bernoulli's equation. It is not in an equilibrium state so its temperature is undefined. If and when it settles down into its new larger volume, however, it is ends up in an equilibrium state. And if it is an ideal gas it will end up at its original temperature.

Now this seems a lot like the entropy of the gas decreased. The process looks irreversible though, so there surely must be a bigger entropy increase somewhere, but where? I suspect it's probably the increase in volume, but in the illustrations in the article the particle beam looks very narrow and the particles pretty localized.

The change in entropy is defined only between equilibrium states. You have not defined your final equilibrium state. The entropy of the gas expanding indefinitely into a vacuum is undefined. If and when it settles down into an equilibrium state with a larger volume, it will have increased entropy.

AM