# Why do gases cool on expansion?

#### R Power

PLEASE someone explain me in detail why gases cool on expansion? yOU may say that when they expand work is done at expense of internal energy but why? Wat is the need to do work when they are not forced to , I mean when they are not given external energy....
Someone please explain the concept to me...
Thnx

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Imagine a gas inside a cylinder containing a freely moveable piston.If the pressure of the gas inside the cylinder is greater then the pressure outside then the gas will expand and do work by pushing the piston out.In terms of collisions,the gas molecules colliding with the retreating piston will bounce off with reduced velocities.Whether you describe it in terms of work done or reducing velocities of the molecules the result is the same ie the gas cools.The cylinder and piston can be dispensed with and the expanding gas will still cool by pushing against the atmosphere.

#### saim_

In addition to above, expansion in empty space or without external resistance will also usually lead to a decrease in temperature, as a result of the Joule-Thomson effect. From wiki:
As a gas expands, the average distance between molecules grows. Because of intermolecular attractive forces (see Van der Waals force), expansion causes an increase in the potential energy of the gas. If no external work is extracted in the process and no heat is transferred, the total energy of the gas remains the same because of the conservation of energy. The increase in potential energy thus implies a decrease in kinetic energy and therefore in temperature.

A second mechanism has the opposite effect. During gas molecule collisions, kinetic energy is temporarily converted into potential energy. As the average intermolecular distance increases, there is a drop in the number of collisions per time unit, which causes a decrease in average potential energy. Again, total energy is conserved, so this leads to an increase in kinetic energy (temperature). Below the Joule–Thomson inversion temperature, the former effect (work done internally against intermolecular attractive forces) dominates, and free expansion causes a decrease in temperature. Above the inversion temperature, gas molecules move faster and so collide more often, and the latter effect (reduced collisions causing a decrease in the average potential energy) dominates: Joule–Thomson expansion causes a temperature increase.
http://en.wikipedia.org/wiki/Joule–Thomson_effect#Physical_mechanism

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#### Naty1

....in detail ...
It's actually NOT a simple question to answer.....all we can do is explain what we observe..not WHY it happens....for example, no one knows why heat exists at all....except it's a form of energy that we experience in this universe....

You'll find one perspective and some useful insights here:

http://en.wikipedia.org/wiki/Kinetic_theory

Instead of the word "velocity" as used by dadface above, if you think of the equivalent "kinetic energy" (1/2mv2...it may make things clearer...and is mentioned in this article.

If the above wikipedia article doesn't "do it" for you try the link to this:

http://en.wikipedia.org/wiki/Equipartition_theorem

In classical statistical mechanics, the equipartition theorem is a general formula that relates the temperature of a system with its average energies.
but agai this is largely what happens not necessarily why....

Another approach which may be conceptually ok but which I suspect has little actual
effect at typical room conditions, would be the application of the Heisenberg uncertainty principle....as you compress molecules they become more energetic...particles don't like being confined...they speed up, get "hotter", having more energy....likewise upon release, they slow down, get cooler along the lines that dadface described....

but WHY that actually happens nobody knows....who made the rule that particles don't like confinement???

#### Andrew Mason

Homework Helper
PLEASE someone explain me in detail why gases cool on expansion? yOU may say that when they expand work is done at expense of internal energy but why? Wat is the need to do work when they are not forced to , I mean when they are not given external energy....
Someone please explain the concept to me...
Thnx
A gas does NOT cool because it expands. That may be the source of your problem. It cools because the gas molecules do work on the surroundings by transferring some of their kinetic energy to the surroundings.

Think of the gas molecules in a container (say an insulated cylinder with a moveable piston on one end). These molecules can only transfer their kinetic energy to the surroundings by individual collisions that move the molecules of the surroundings outward. They have no means of moving them inward. So when they transfer energy to the surroundings, the molecules of the surroundings move outward. When the surroundings acquire this energy (eg. the piston moves outward) the molecules of the gas lose energy. That is just conservation of energy (which is the essence of the first law of thermodynamics). It also happens that the volume increases.

If an ideal gas were to simply expand without doing any work on surrounding molecules (eg. a free expansion of gas into a vacuum) there would be no change in energy of the gas molecules (no cooling).

AM

#### pallidin

A related experiment:
Take a good size rubber band and, holding it close to your lips, pull it and then quickly press the pulled rubber band against your lip.
Your lip senses hot.

Keeping the band stretched, remove it from your lip and let it spring back to normal, then touch it again to your lip.
Your lip senses cold.

Or is that the other way around?

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#### CyberShot

I'm thinking there's a remarkably simple answer to the OP's question.

If you increase the volume of a balloon of gas, the atoms inside are less likely to hit each other and thus the average kinetic energy goes down, and thus the temperature decreases.

#### Andrew Mason

Homework Helper
I'm thinking there's a remarkably simple answer to the OP's question.

If you increase the volume of a balloon of gas, the atoms inside are less likely to hit each other and thus the average kinetic energy goes down, and thus the temperature decreases.
This is not correct. Whether the atoms hit each other or not does not change the total kinetic energy of the molecules of the gas. If the gas expands without doing work on the surroundings, there is no change in temperature at all. So if you place the balloon in a vacuum, the gas expands without doing work on the surroundings (ignoring the work on the balloon itself) so its temperature does not decrease.

AM

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#### lalbatros

R Power,

It would be better to say that gases lose energy when they provide work during expansion.
The statement is a relation between energy (of the gas) and work being done (by the gas).
It is simply the law of energy conservation.

Losing energy will imply cooling down.
But if no work is done, there could still be a cooling effect for "real gases".
This occurs when the enthalpy depends not only on the temperature but also on the pressure: H(p,t).
For perfect gases, the enthalpy does not depend on the pressure and no work implies no cooling.

Considering the microscopic interpretation, you could intuitively guess that attraction between molecules of the gas will imply a cooling during free expansion (ie no work epansion). This means a positive Joule-Thomson coefficient.

___
Thanks, Andy Resnik, for the interresting paper on negative Joule-Thomson coefficient!

#### R Power

If an ideal gas were to simply expand without doing any work on surrounding molecules (eg. a free expansion of gas into a vacuum) there would be no change in energy of the gas molecules (no cooling).
This makes sense.... but then what about the following explanation:
As a gas expands, the average distance between molecules grows. Because of intermolecular attractive forces (see Van der Waals force), expansion causes an increase in the potential energy of the gas. If no external work is extracted in the process and no heat is transferred, the total energy of the gas remains the same because of the conservation of energy. The increase in potential energy thus implies a decrease in kinetic energy and therefore in temperature.

#### Andrew Mason

Homework Helper
This makes sense.... but then what about the following explanation:
In a real gas, as opposed to an ideal gas, there are attractive forces between atoms. These can cause some of the atoms to bind to each other in a low energy collision. As a result, some of the energy in the gas may be used to overcome binding energies before adding kinetic energy. As a result some internal energy is "potential" energy. For an ideal gas this does not apply (hence my reference to "ideal gas" in the passage you quoted.

AM

#### CyberShot

Sorry, I should've clarified my statement.

Imagine two gases with all else equal except one was contained in a container twice the volume of the other. In the smaller container, you can imagine the atoms knocking the ends of the container more frequently.

Repetitive collisions between the atom and container should into the ends should heat up the gas

#### Andrew Mason

Homework Helper
Sorry, I should've clarified my statement.

Imagine two gases with all else equal except one was contained in a container twice the volume of the other. In the smaller container, you can imagine the atoms knocking the ends of the container more frequently.

Repetitive collisions between the atom and container should into the ends should heat up the gas
This is also quite incorrect. Energy has to come from somewhere. If the container and gas are at the same temperature and there is no heat flow into gas and no work being done on the gas, the collisions between the atoms and container cannot heat up the gas or the container.

Now if one compresses the gas in an insulated container its temperature will increase. That is because work is done on the gas - energy is added to the gas. So from the first law (conservation of energy) there must be an increase in internal energy because energy (work) is added and there is no heat flow in or out (adiabatic).

If you are interested in the mechanism by which work is done on the gas, you have to think of the molecules of the gas hitting a container wall that is moving toward the molecule and has a force being applied to it. What happens to the momentum change of a molecule striking such a wall compared to the momentum change of a molecule striking a fixed non-moving wall? The converse happens when the wall is pushed outward by the molecules colliding with the wall.

AM

#### Naty1

Andrew Mason: good posts, right on!!!! Thank you.
glad I posted: "...It's actually NOT a simple question to answer..."

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