Again with the Force

[Phil153]

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Here, you say "The force primarily responsible is my throw, as it's the only thing that gave energy to the dice." What is the nature of the force associated with your throw?

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You missed the point completely on that example. May as well say the strong and weak nuclear forces are the forces responsible for everything on Earth as without them the sun wouldn't create carbohydrates and we wouldn't be throwing dice.

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You are focused on who is right and who is wrong. I'm looking for understanding, not just the answer. I'd rather not let my ego get in the way, but your tone makes that difficult.

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This isn't about ego. This is such an unbelievably simple phenomena to even a layman that the replies in this thread amazed me. The fact that a physics teacher quoted the second law as being relevant astounded me. The simple answer is this: To a very good approximation, gases are like billions of tiny balls spread far apart relative to their size, each with different velocities. At room temperature they travel at high speed. If you look at it that way, it's exceedingly obvious why diffusion occurs and why you can very quickly smell perfume across a room. And why particular forces aren't relevant to the basic mechanism of diffusion. They teach the kinetic model of gases in 8th grade and it should be common knowledge to anyone who's reached high school.

Anyway, I apologise for being amazed.

[uDevil]

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I don't know what you mean by internal temperature. The temperature is independant of the pressure.

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Oops, sorry about that. Temperature is proportional to the product of pressure and volume. However, (as ChrisV said) increased pressure doesn't imply increased temperature if the volume is allowed to decrease.

[Matt R.]

OK, I will try this again. First of all, let me say that the tone in the my first post was a result of some posts made towards the OP and Chips, even by some people with admittedly zero physics background. Instead of intelligent debate we get snotty attitudes and attacks on people making good replies. All of this despite:

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This is a very interesting question which intrigued great physicists such as Maxwell, Boltzmann and Liouville. Even modern day physicists who work on chaos find inspiration by posing this question.

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So this is not a straightforward question, and pretending it is while ignoring posts by university-level lecturers is just stupid.

We all seem to be looking at this problem from different angles, which lead to the same conclusion. First a quote from Dr. Wong:

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However, after all, why do molecules move with different speed? If, instead, all molecules move with the same speed, they will march like an army everywhere in space, and there should be no diffusion. The answer is that molecules exert forces on one another, and these forces transfer momenta among them.

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So a PREREQUISITE for diffusion to occur is that all molecules must be bouncing around, transferring momentum to one another. And for this to occur, some force must be mediating the transfer of momentum between the molecules. This would be primarily the electromagnetic force. Theoretically take this force away, and:

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If, instead, all molecules move with the same speed, they will march like an army everywhere in space, and there should be no diffusion.

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And I enjoyed how Copernicus clarified this sentence:

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Rather, forces (of any nature) are needed to cause momentum transfer molecules, which in turn give rise to the phenomenon of diffusion.

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by blatantly removing the author's mention of the concept of FORCE being required for the momentum transfer between molecules.


OK, now for a couple of questions. uDevil, you mentioned that there is no net force on the molecules. In a pressurized canister, I agree as the molecules are just bouncing around and transferring momentum, but with no net direction of force. There is an equal probability that any molecule will experience an equal force from any direction. But consider what happens when a highly pressurized canister explodes. How can there be ZERO net force on the molecules on the outside of the canister when it blows up? The wall of the canister was clearly applying a force to the outer "edges" of the gas, keeping the gas as a whole confined to the space. When you remove the force of the wall, what is replacing it for there to be zero net force? The gas molecules outside the canister obviously don't provide an equivalent amount of resistance when the canister explodes. IMO, the clear answer is that the molecules further inside the canister are colliding with the molecules on the fringe of the mass of gas molecules, and since there is no wall now hindering their diffusion into the open space, it pushes the molecules on the edge away. You can now imagine a limit of this effect continually pushing the molecules away from one another, distributing them evenly in the room. Now, what force mediates this interaction? I believe it is primarily electromagnetic. You can solve problems like this simply using probability as others are saying, but that in no way implies there is no force mediating the momentum transfer between particles (which is *necessary* for diffusion to occur).

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I don't know what you mean by internal temperature. The temperature is independant of the pressure. The kinetic energy of the molecules doesn't depend on the pressure.

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The temperature is not independent of the pressure. PV/nR = T, p is pressure T is temperature. Increasing the pressure of a gas will increase its temp. And kinetic energy of a gas is directly related to its temperature. By pressurizing a gas, you will increase its kinetic energy.

To prove once and for all that a force is present BY DEFINITION during diffusion:

You have an insulated box divided into 2 compartments of equal volume, V. One compartments contains n moles of ideal gas, the other is empty. When we break the partition, the gas diffuses into both compartments.

Now, entropy change depends only on the initial and final states of the system. So what we have in this case is an isothermal expansion from V to 2V at a constant temperature T. The gas does work during the expansion, as W = (integral)p dV. And from the ideal gas law, p = nRT/V. This leaves us with.

W = nRT (integral) dV/V = nRT ln (Vf/Vi)

ln (Vf/Vi) > 0, so the gas does a positive amount of work. Now, what is work, by definition? W = F.s. W = work, F = force, and s = displacement.

Work is non-zero, so there MUST be some force acting on the molecules during the expansion. This is by definition. If you have an issue with this, you may need to take it up with Isaac Newton's definition of force.

In summary, I think what Dr. Wong and some posters are doing is simply evaluating the problem using a probabilistic argument. This is fine I think, because ultimately the momentum transfer collisions between particles are based on probability (the further apart they are, the lower the probability of a collision... etc.). But this in no way implies that no force is responsible for the process of diffusion, just that it may be an unnecessary step in analyzing the process at a macroscopic level.

[uDevil]

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Here, you say "The force primarily responsible is my throw, as it's the only thing that gave energy to the dice." What is the nature of the force associated with your throw?

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You missed the point completely on that example. May as well say the strong and weak nuclear forces are the forces responsible for everything on Earth as without them the sun wouldn't create carbohydrates and we wouldn't be throwing dice.

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You have made the same point more than once. That I haven't accepted it yet doesn't mean I missed it.

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This isn't about ego. This is such an unbelievably simple phenomena to even a layman that the replies in this thread amazed me. The fact that a physics teacher quoted the second law as being relevant astounded me. The simple answer is this: To a very good approximation, gases are like billions of tiny balls spread far apart relative to their size, each with different velocities. At room temperature they travel at high speed. If you look at it that way, it's exceedingly obvious why diffusion occurs and why you can very quickly smell perfume across a room. And why particular forces aren't relevant to the basic mechanism of diffusion. They teach the kinetic model of gases in 8th grade and it should be common knowledge to anyone who's reached high school.

Anyway, I apologise for being amazed.

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Amazement is coming across as contempt. Calling an idea simple, clear, or obvious doesn't make it so. Contempt for those who fail to understand helps create the lack of understanding that produces the contempt.

What is being taught in schools may resemble the kinetic theory of gases, but it is really a process where students are fed answers and expected to regurgitate them on command. Asking questions is discouraged by the instructor's need to move on to the next topic, his own lack of understanding, or displays of contempt.

That at the end of long exposure to such a process so few people fully understand diffusion seems unsurprising to me. You could ask a whole series of similarly basic questions and find a similar situation.

[ChrisV]

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The temperature is not independent of the pressure. PV/nR = T, p is pressure T is temperature. Increasing the pressure of a gas will increase its temp. And kinetic energy of a gas is directly related to its temperature. By pressurizing a gas, you will increase its kinetic energy.

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How do you plan to pressurise the gas? You can do it by decreasing volume, in which case the temperature will not increase. Or you can do it by heating it, in which case, unsurprisingly, the temperature increases.

[Matt R.]

I originally was not talking about the act of pressurizing a gas. My point was that if you take 2 equivalent canisters of gases (volume, # moles, etc.), the one that is more highly pressurized must have a higher temperature.

I was connecting this idea of a highly pressurized/high temp canister as one that exerts a lot of force on the walls of the canister. If the molecules have such a high kinetic energy that they are close to making the walls of the canister bust, they must be exerting a lot of force on other molecules as well. When the canister does break, the molecules spread out very rapidly in an explosion because of this force being exerted during the high energy collisions.

[Alex-db]

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How do you plan to pressurise the gas? You can do it by decreasing volume, in which case the temperature will not increase...

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Try putting your thumb over the end of a bicycle pump, quickly decrease the volume (push the pump), and see whether the temperature of the air against your thumb has increase.

[Matt R.]

I was about to respond to that as well. I originally read it as "the temperature will increase".

The temperature most definitely does increase when you decrease the volume... I'm not sure what else to say about the statement.

Maybe when I get a grasp on basic Physics, I can start arguing with Maxwell and Boltzmann about the relevance of these "simple" physics problems.

PS -- ChrisV, please go take physics 1, then maybe physics 2 if you aren't too smart for it. Then come back and post in this thread when you can actually provide some insight.

[jason1990]

Suppose that initially the perfume bottle is in the corner of the room. Then initially, the center of mass of the perfume molecules is also in the corner of the room. When the perfume bottle is opened and the particles begin diffusing, the center of mass will move towards the center of the room, as the particles distribute themselves uniformly. So a net force is acting on the particles. This net force is the difference between the forces applied by walls near the bottle and walls far from the bottle. Walls near the bottle will initially receive more collisions and apply more force to the system of particles. If there were no walls (or the bottle was initially in the center of the room), then the particles would diffuse evenly in all directions, the center of mass would not move, and there would be no net force. I suspect, however, that this observation is not relevant to your original question. If it's not, then sorry for interrupting your lively thread. [img]/images/graemlins/smile.gif[/img]

[ChrisV]

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How do you plan to pressurise the gas? You can do it by decreasing volume, in which case the temperature will not increase...

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Try putting your thumb over the end of a bicycle pump, quickly decrease the volume (push the pump), and see whether the temperature of the air against your thumb has increase.

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I am aware that applying pressure to a gas causes its temperature to increase. What I'm saying is that there is no particular reason that a gas at high pressure has to have a higher temperature. Here again is Matt R's original statement:

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Think of a canister under high pressure. A gas under high pressure is at a higher internal temperature than one under low pressure, and thus the particles have a higher kinetic energy.

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"A gas at high pressure is at a higher temperature" is false and is not the same statement as "applying pressure to a gas causes its temperature to increase".