There is little molecule bond between gas molecules, then why we have

[Jackson Lee]

Hey, guys, I have just watced a fantastic animation of the microscopic process of sound wave traveling, in which model was described as many balls connected by springs.
But the problem is what we learned in thermodynamics chapter is that there is no bonds between molecules in gas, then how could we use this model. However, this model could explain process of sound propagates perfectly. I feel puzzled.

 

[voko]

Let's get terminology right first.

Thermodynamics does not study molecules or atoms.

Kinetic theory of gases makes use of molecules, and in its simplest accounts, interaction between molecules is often neglected. Obviously, such simplified versions cannot explain sound in gases.

The model presented in the video, on the other hand, completely ignores the chaotic motion of molecules in a gas. This is another kind of simplification.

 

[maheshshenoy]

such simplified versions cannot explain sound in gases.

But I checked in most sites, that mention the motion of sound waves in ideal gas. For example in wiki
http://en.wikipedia.org/wiki/Speed_of_sound#Compression_and_shear_waves
it mentions a line saying the "speed of sound in an ideal gas is independent of the frequency"

So I guess, in ideal gas, we use the collision as the basis for the transfer of energy from one molecule to another?

like Newton's cradle ? Perfect Elastic collisions?

 

[voko]

So I guess, in ideal gas, we use the collision as the basis for the transfer of energy from one molecule to another?

Normally, yes. But I have also seen introductions into the kinetic theory where molecules interact only with the walls of the (imaginary) container; this may be what Jackson Lee was taught, but I am guessing here.

 

[maheshshenoy]

Normally, yes. But I have also seen introductions into the kinetic theory where molecules interact only with the walls of the (imaginary) container; this may be what Jackson Lee was taught, but I am guessing here.

True.. however, we do that just to simplify things, and also usually its mentioned, that even though in reality there are collisions of molecules with EACH OTHER, the final result (connecting the pressure, volume and the moles and rms speed) remains the same. So we only avoid the collision of molecules with each other and only consider with the container to make the derivation simpler.
right?

 

[voko]

That is right, with a caveat. What you describe is yet another model of reality, not the reality itself. Interaction of molecules in a real gas is far more complex than billiard-ball like collisions (for that matter, real billiard ball collisions are also very complex if one tries to account for every known aspect).

 

[maheshshenoy]

interaction of molecules in a real gas is far more complex than billiard-ball like collisions

Indeed, but we are talking about how can we think about sound wave in an ideal gas (which apparently have no force of attraction). So I was just using collision as a way of explaining the propagation of longitudinal waves :)

 

[sophiecentaur]

@ Jackson Lee
Do you have any comments on what's been written so far? It's useful to have some feedback to avoid the thread developing a life of its own and going off in a direction that the OP just can't follow.

 

[Jackson Lee]

@ Jackson Lee
Do you have any comments on what's been written so far? It's useful to have some feedback to avoid the thread developing a life of its own and going off in a direction that the OP just can't follow.

Sorry, I was too tired yesterday so I took a nap after posting that thread. Now I am pleased with what a good job that our two friends did.

 

[Jackson Lee]

Let's get terminology right first.

Thermodynamics does not study molecules or atoms.

Kinetic theory of gases makes use of molecules, and in its simplest accounts, interaction between molecules is often neglected. Obviously, such simplified versions cannot explain sound in gases.

The model presented in the video, on the other hand, completely ignores the chaotic motion of molecules in a gas. This is another kind of simplification.

Yes, thermodynamics doesn't study molecules or atoms, but they are real participants of thermal exchange process, especially in something, such as ideal gas. You said these two models are just two different simplified versions of the reality. Do you mean there did deviations from truth in both of there two versions but both of their deviations are in limited extent?

 

[Jackson Lee]

Indeed, but we are talking about how can we think about sound wave in an ideal gas (which apparently have no force of attraction). So I was just using collision as a way of explaining the propagation of longitudinal waves :)

Actually, I tried to use perfect collision theory to explain propagation of sound just like you some time ago, however something followed confused me totally.
For example, if sound waves could be propagated by collision, then how to explain such regular sinusodial displacement pattern existed within these molecules? It should never appear like this if sound waves really propagate via collisions. Besides the sinusodial pattern reminded me of simiple harmonic oscilation.

But if there is strong molecule bonds between gas molecules, then how to explain random movement which is defined for gas molecules in microscopic thermodynamic analysis.
Maybe what voko said is correct, both of these model is not perfect. I hope more people to involve in this open-ended topic to delve in the truth of nature.

 

[AlephZero]

The usual way to cut through the tangle you seem to be in, is to divide it into two parts.

1. Start with the assumptions of kinetic theory of an ideal gas, and derive some of the standard gas laws, in particular the relationship for adiabatic changes, $PV^\gamma = \text{constant}$.

2. Assume the gas is a continuous medium and use that equation, plus Newton's laws of motion, to get the wave equation for sound propagation.

Your "two ideas" in the previous thread look like personal speculation (and they are both wrong). If you read the forum rules, you will see that the purpose of PF is to discus mainstream physics. If you can provide a reference to a peer-reviewed paper or a textbook to support those two ideas, that's fine. Otherwise, they are off limits.

 

[Jackson Lee]

Hey, guys, I found this interesting explanation. If you are interested in this topic, you could read it.
http://van.physics.illinois.edu/qa/listing.php?id=2056
And I will contact my teacher, if there are any better explanation. I will post it here.

 

[voko]

Actually, I tried to use perfect collision theory to explain propagation of sound just like you some time ago, however something followed confused me totally.
For example, if sound waves could be propagated by collision, then how to explain such regular sinusodial displacement pattern existed within these molecules? It should never appear like this if sound waves really propagate via collisions. Besides the sinusodial pattern reminded me of simiple harmonic oscilation.

Representation of sound via a sinusoidal oscillation is also a simplification. Real sounds are never sinusoidal, but they can be represented as a sum of infinitely many sinusoidal oscillations of different frequencies. Even staying within this simplification, the displacements are not within molecules; in fact, there are no displacements you can sensibly talk about in the context of sound propagation in fluids (solids are simpler to understand).

A gas, in an absence of sound and otherwise in equilibrium within a container, is a chaotic motion of molecules, colliding with one another and the walls of the container. Pressure, which is a measure of the average speed of molecules, is everywhere the same.

When sound propagates through the gas, pressure is no longer identical everywhere. In some places it is higher, in some places it is lower; this is the compression/rarefaction wave mentioned in the video. That means that the average speed of molecules gets higher or lower as sound propagates.

Note it is pointless to try to understand propagation of sound by looking at individual molecules. Motion of individual molecules is simply chaotic, sound or not. It is only with large numbers of molecules, when you can meaningfully talk about average speeds and consequently about pressure, that you can explain propagation of sound.

 

[Jackson Lee]

Representation of sound via a sinusoidal oscillation is also a simplification. Real sounds are never sinusoidal, but they can be represented as a sum of infinitely many sinusoidal oscillations of different frequencies. Even staying within this simplification, the displacements are not within molecules; in fact, there are no displacements you can sensibly talk about in the context of sound propagation in fluids (solids are simpler to understand).

A gas, in an absence of sound and otherwise in equilibrium within a container, is a chaotic motion of molecules, colliding with one another and the walls of the container. Pressure, which is a measure of the average speed of molecules, is everywhere the same.

When sound propagates through the gas, pressure is no longer identical everywhere. In some places it is higher, in some places it is lower; this is the compression/rarefaction wave mentioned in the video. That means that the average speed of molecules gets higher or lower as sound propagates.

Note it is pointless to try to understand propagation of sound by looking at individual molecules. Motion of individual molecules is simply chaotic, sound or not. It is only with large numbers of molecules, when you can meaningfully talk about average speeds and consequently about pressure, that you can explain propagation of sound.

Yes, we should analysis the process from macroscopic view. But what puzzled me initially is its sinusodial wave pattern when the wave source vibrates sinudodially, especially when there is few molecule bonds between gas molecules. Even if from macroscopic view, there must be a restoring force as the source of simple harmonic oscillation. Therefore, if you are interested in this, I recommend you read this. http://van.physics.illinois.edu/qa/listing.php?id=2056
Finally, I want to express my deep appreciation to you for your amazing participation. You helped me a lot. Thanks

 

[voko]

Even if from macroscopic view, there must be a restoring force as the source of simple harmonic oscillation.

The restoring force is given by the difference in pressure between two small (but still macroscopic) regions. It causes gas in higher pressure regions to expand into lower pressure regions, which increases pressure in the formerly lower-pressure regions, etc.

 

[Jackson Lee]

The restoring force is given by the difference in pressure between two small (but still macroscopic) regions. It causes gas in higher pressure regions to expand into lower pressure regions, which increases pressure in the formerly lower-pressure regions, etc.

What I want to say is this:

The molecules have some inertia, so they in fact go a bit farther than it would take to even out the pressure, and the pressure in that little region where the pressure was initially higher becomes lower than the average pressure in the liquid, and the molecules are pulled back where they started.

Maybe I should stress it out earlier. I hope it will be meaningful to you.

 

[sophiecentaur]

Exactly the same Equations will describe waves of all types, as long as the system is linear. The interactions between molecules and the departure from an ideal gas will have the effect of introducing non linearity and loss factors into the simple masses-linked-by-springs model. That means that, when the pressure of the gas is relatively low and the gas is far from condensing, any gas will behave ideally. As the pressure increases, the proximity of the molecules will start to affect the simple model. For very high levels of sound, the density in the peaks of pressure (in particular) will no longer relate linearly to the average displacement of the molecules because the energy is not just kinetic but Potential.
By introducing your statement that "Molecules have some inertia" you are falling into the trap of hopping and out between macroscopic and microscopic models. This is very risky, imo. What happens when two molecules approach within their range of influence will depend upon the specific substance but it can be modeled in terms of a proportion of the system energy being transformed to potential. Positive potential mountains of finite width, as opposed to Potential Wells, will surround each molecule's location, causing mutual repulsion.

 

[Jackson Lee]

Exactly the same Equations will describe waves of all types, as long as the system is linear. The interactions between molecules and the departure from an ideal gas will have the effect of introducing non linearity and loss factors into the simple masses-linked-by-springs model. That means that, when the pressure of the gas is relatively low and the gas is far from condensing, any gas will behave ideally. As the pressure increases, the proximity of the molecules will start to affect the simple model. For very high levels of sound, the density in the peaks of pressure (in particular) will no longer relate linearly to the average displacement of the molecules because the energy is not just kinetic but Potential.
By introducing your statement that "Molecules have some inertia" you are falling into the trap of hopping and out between macroscopic and microscopic models. This is very risky, imo. What happens when two molecules approach within their range of influence will depend upon the specific substance but it can be modeled in terms of a proportion of the system energy being transformed to potential. Positive potential mountains of finite width, as opposed to Potential Wells, will surround each molecule's location, causing mutual repulsion.

Frankly speaking, I am unfamiliar with what you said, so I emailed my professor about this topic. If there is any better explanation, I will post it here.

 

[sophiecentaur]

Frankly speaking, I am unfamiliar with what you said, so I emailed my professor about this topic. If there is any better explanation, I will post it here.

And cue Professor. Click. . . .

 

[anhtho]

At normal conditions, say at atmospheric pressure, gas molecules still collide with each other frequently, so they 'link' together via collision, so that sound can travel.
In vacuum or nearly vacuum condition, the collision number is small, then sound can not travel.