## Main Question or Discussion Point

Hi,

When a hot and dense fluid suddenly expands, how much can it cool down.

Lets take for example an expansion valve from an AC, does the fluid do work when passing through the valve or does it not even need to do work in order to cool down.

What is the lowest temperature that the fluid can cool down to?

I hope I've been clear enough, thanks.

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jfizzix
Gold Member
From a practical standpoint, cooling this way will be limited by your ability to insulate your regrigerator and its components. The physical process doesn't have a minimum working temperature (besides absolute zero).

If I understand what you're talking about, that process would be the Joule Thompson process (used in refrigeration). In this case, there is no work done on the gas, and the cooling is due to the intermolecular forces between individual molecules in the gas.

Most cold gases will cool further under expansion (through a valve) because as the atoms get further away from one another, the average potential energy increases (because far away, the force is attractive). Since total energy is conserved, the average kinetic energy decreases, and the temperature goes down.

However, this cooling doesn't occur at all temperatures. At temperatures above what's called the inversion temperature, the reverse will happen. This is because the average (in time) potential energy depends on the rate of collisions.

At higher temperatures, the atoms are moving faster, and collide with one another more often.

If a pair of atoms are close enough to each other, the force between them will be repulsive, and the potential energy will have a net decrease when they are far away enough from each other again.

If the cloud of atoms are on average close enough to each other, expanding the gas will lead to a net decrease in potential energy, and a net increase in average kinetic energy (assuming energy is conserved)

This inversion temperature is different for each gas, and is usually found experimentally.

For example:, the inversion temperatures of nitrogen and oxygen are over $500K$, so you could keep cooling them until they liquify starting at room temperature (provided good insulation).

Last edited:
Thanks a lot for the answer, that's exactly what I wanted, could you please tell me how much this temperature change is in one cycle is it a small amount and needs to be repeated or can it be large with the right substance?

And also, the inversion temperature must be above room temperature in order to be able to cool down to anything you want right?

jfizzix
Gold Member
Unfortunately, I don't know what the temperature change per cycle would be. It may help to look up the Linde cycle, which is an ideal model of a refrigerator based on this process.

The inversion temperature needs to be above your starting temperature to do any cooling. If you start at room temperature, then yes. Otherwise, you could use some other cooling mechanism to get down to a better starting temperature.

Thank you, you are very helpful I wish I could somehow give you a thumbs up or something :)

jfizzix
Gold Member
you can, "like" my post, if you prefer.

From a practical standpoint, cooling this way will be limited by your ability to insulate your regrigerator and its components. The physical process doesn't have a minimum working temperature (besides absolute zero).

If I understand what you're talking about, that process would be the Joule Thompson process (used in refrigeration). In this case, there is no work done on the gas, and the cooling is due to the intermolecular forces between individual molecules in the gas.

Most cold gases will cool further under expansion (through a valve) because as the atoms get further away from one another, the average potential energy increases (because far away, the force is attractive). Since total energy is conserved, the average kinetic energy decreases, and the temperature goes down.

However, this cooling doesn't occur at all temperatures. At temperatures above what's called the inversion temperature, the reverse will happen. This is because the average (in time) potential energy depends on the rate of collisions.

At higher temperatures, the atoms are moving faster, and collide with one another more often.

If a pair of atoms are close enough to each other, the force between them will be repulsive, and the potential energy will have a net decrease when they are far away enough from each other again.

If the cloud of atoms are on average close enough to each other, expanding the gas will lead to a net decrease in potential energy, and a net increase in average kinetic energy (assuming energy is conserved)

This inversion temperature is different for each gas, and is usually found experimentally.

For example:, the inversion temperatures of nitrogen and oxygen are over $500K$, so you could keep cooling them until they liquify starting at room temperature (provided good insulation).