[seriously disabled]

It is known that when a gas expands it cools down. But why does the decrease in pressure cause the molecules of the gas to slow down?

[Klaynos]

To expand takes energy. This energy has to come from the internal energy of the gas.

[swansont]

Uri said:

It is known that when a gas expands it cools down. But why does the decrease in pressure cause the molecules of the gas to slow down?

PV = nRT (ideal gas)

You can get the decrease in pressure from an increase in volume, decrease in number of atoms or a decrease in temperature. Under the circumstances of constant volume and number of atoms, the decrease, as Klaynos has said, must come from a decrease in energy, reflected by a decrease in temperature.

[iNow]

Doesn't it basically mean that the molecules don't bump into one another as often? Like the difference between walking through a restaurant and a rock concert... the density of people at the concert means you bump into more of them and take on more heat? When you bump into fewer people (less density... post-expansion) you cool off.

[swansont]

iNow said:

Doesn't it basically mean that the molecules don't bump into one another as often? Like the difference between walking through a restaurant and a rock concert... the density of people at the concert means you bump into more of them and take on more heat? When you bump into fewer people (less density... post-expansion) you cool off.

Yes - as the atoms or molecules slow, they undergo fewer collisions with the container walls per unit time. The collisions are also at a lower momentum.

[Mr Skeptic]

Consider that the expanding gas does work, and so has less energy. If you move the walls back the gas is exerting a force (pressure times area) over a distance (however far you move the walls), which is work. Since the gas has less energy after expanding, it is no surprise that its temperature will be lower.

[Martin]

Uri said:

It is known that when a gas expands it cools down. But why does the decrease in pressure cause the molecules of the gas to slow down?

This is fun. It is like the seven wise men and the elephant---each person tells a different aspect. of the same thing really.

I will tell you another way to visualize it. Imagine the gas in a cylinder with perfectly reflecting walls. To reduce the pressure, draw the piston back.
Gas molecules get slowed by bouncing off a receding "mirror".

You asked what causes the molecules to slow down. What causes them to slow down is bouncing off a receding piston-face "mirror".

You see the molecule come at the mirror with veloc. V and the mirror backing off with much smaller veloc. v. This is just a classic Galileo thing, not sophisticated.
The mirror sees the particle come with velocity V-v
and it sends the particle back with what it thinks is velocity -(V-v), i.e. in the opposite direction. But from your lab perspective what it calls -(V-v) is
actually -(V-v)+v = -(V-2v).

So twice the mirror's speed has been deducted from the molecule's speed (taking absolute value now.)

If a molecule happens to strike the mirror with exactly twice the speed that the mirror is receding, that molecule will be stopped dead. It will come off the mirror with zero speed in lab coordinate. What a temperature drop. It totally chills out!

I'm picturing this is a one-dimensional version for simplicity, everything along a horizontal axis.

[CaptainPanic]

Mean velocity of a gas molecule is only governed by temperature.

When you expand a gas, it cools down, so that slows the molecules.

But if you compare two molecules, one in say 1 bar, the other in 0.5 bar, both at the same temperature, then they'll have the same (average) velocity.

There is a formula to calculate the mean velocity of a gas molecule (and some more formulas to calculate something almost the same, their differences have to do more with statistics than with physics):



Note that pressure is not in this formula. Attempting to substitute the R*T using the ideal gas law will give you:



And in this second formula, the pressure is included, but it is divided by n, and multiplied by V. The term n/V is the number of molecules per volume.

You see that in this substituted version, the molecule density (pressure) still cancel.

[Shadow]

Incidentally, the very same question was posed today in our class, and our teacher answered in a manner which seems pretty logical to me. The walls of the object in which the gas is contained are moving away, and thus when the gas molecules impact the walls, they rebound with a smaller velocity. Hope that makes sense :D

[Martin]

Your teacher chose the same explanation I did.:D

Martin said:

...
You asked what causes the molecules to slow down. What causes them to slow down is bouncing off a receding piston-face "mirror"....

I think there are several explanations some more abstract some less, all pretty much equivalent at the root.

[Jacques]

I don't think that the molecule necesserly slow down.
For example take a cylinder with a wall in the centre. One side of the wall is filled with air at ambient temperature and pressure and the other side is empty. Remove the wall (there is no receding wall).
The pressure is now half the ambient pressure and the volume is doubled. From PV=nrT,
T should be the same.

[swansont]

Jacques said:

I don't think that the molecule necesserly slow down.
For example take a cylinder with a wall in the centre. One side of the wall is filled with air at ambient temperature and pressure and the other side is empty. Remove the wall (there is no receding wall).
The pressure is now half the ambient pressure and the volume is doubled. From PV=nrT,
T should be the same.

You can certainly do this isothermally, which is why I was trying to point out in a prior post it's important to specify what variables are held constant. But expansion isn't necessarily free expansion. That wasn't specified in the OP, but the temperature change was, and I think everyone has been assuming that case.

One thing to remember about thermo is that knowing the starting and finishing values of a variable isn't enough. You have to hold some variable constant and/or it matters how you get from state A to state B. So you can't just say "when a gas expand, it cools" because that's not universally true. (and keeping track of all that is why I find thermo to be such a pain)

[CaptainPanic]

Why would the walls move away? In a piston, you'd have to move the walls away pretty fast to make a serious impact on the movement of the molecules. Typical laboratory piston setups move the walls rather slow.
As a comparison, your average gas molecule (nitrogen () at room temperature) moves around at a mean velocity of:

m/s

Obviously, car engines do have pistons that move fast enough (Formula 1 engines reach 10000 rpm. Say their pistons are moving 30 cm, then they do 50 m/s (average speed). That's 10% of the nitrogen's velocity at room temperature.

Anyway, I still suggest using the kinetic theory of molecules (link 1 and link 2) to describe why molecules slow down... the moving wall theory totally fails to describe what happens in case of a relief valve where there are no moving parts, but where the gas itself escapes some container into a bulk environment (atmosphere).

[mabsj2]

When pressure is reduced, it means expansion has taken place. expansion requires energy to take place. and this energy is got from the surrounding molecules.

[CaptainPanic]

mabsj2 said:

When pressure is reduced, it means expansion has taken place. expansion requires energy to take place. and this energy is got from the surrounding molecules.

Although every process requires energy to take place... the energy is already put into the system before the expansion. The compression needs energy to take place... and that energy can come from pretty much anywhere.

A compressor is a machine that can turn a low pressure gas into a high pressure gas. This needs energy.

If you then expand a gas, it usually cools down. You can also do an isothermal expansion (an expansion at constant temperature). In that case, the entropy effects are the only thing that matter (and still, the energy changes, but the enthalpy remains practically the same).

Expansion is the phenomena where gas molecules get more space to move. Therefore they make less collisions against any solid object nearby, and that is what we observe as a reduction in pressure.

Compression is the phenomena where gas molecules get less space to move. Therefore they make more collisions against any solid object nearby, and that is what we observe as an increase in pressure.

Now, this increase in pressure... imagine that you want to increase the pressure. Simply imagine a bottle with air. Squeeze it and you compress the gas. Once the gas is a little compressed, more molecules hit the inside of the bottle than the outside. Therefore, a net Force exists that pushes outward (against you squeezing). Since you also move the walls of the bottle, you apply a force, and the walls move. Force * distance = Work.