Again with the Force

[uDevil]

Matt,

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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....

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I think you're on the wrong track by thinking about pressure. I say this because diffusion would occur even if there is no pressure difference:

Imagine that you could select a small volume of air in a room and mark each of the molecules in that volume so that you can follow them around the room. Now there is no pressure difference between the selected volume and the rest of the room. (The molecules in the selected volume are of the same type as those in the rest of the room, so there is no difference in partial pressure either.)

Now observe the marked molecules at some later time. They will have become evenly distributed around the room.

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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.

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I admit this confuses me. I think it depends on how you define the system. For an isolated system (no matter energy or energy can cross the system boundary), there are no (one? anyway the state of the system is fixed once you set it up) independent variables. On the other hand, in an open system, there are 3 independent variables because I am allowed to add or remove gas molecules and energy, and change the volume as I please.

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Increasing the pressure of a gas will increase its temp.

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If you increase the pressure by decreasing the volume and the system is not adiabatic (so heat may cross the boundary), the rise in temperature will be a transient phenomenon and the gas temperature will drop back down to match that of the environment while the pressure remains elevated.

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The gas does work during the expansion....

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I don't see how the gas does work as it is not expanding against an applied force.

BTW, ChrisV merely said he didn't take Physics 1 (we used to call that "bozo physics"). He probably just skipped it as it seems clear to me he has a very good understanding of the topic.

I encourage you to keep thinking about this. Despite what others have said or implied, this is NOT easy.

[Chips_]

Good post Jason1990. You are thinking clearly about the situation.

[Matt R.]

Chris,
PV = nRT, the ideal gas equation states that if you have 2 samples of the same gas, and the samples are of equal volume and equal number of moles, then the sample with the higher pressure must have the higher temperature, and vice versa. It's just an equality,

PV/nR = T, let V/nR = C be a constant
C*P = T, so pressure varies directly with temperature.

My original statement implied that V/nR was a constant between the 2 canisters of gas, otherwise my statement was useless (and I explicitly stated I meant they were constant in later posts). Again, I was just trying to show a relation between the internal temperature (and pressure) of a gas and its kinetic energy, leading to an increased force exerted on the walls of the canister.

uDevil,
That's the thing (about pressure). A gas will ALWAYS exert a pressure, and therefore a force, against the walls of any container that it is held in. Even if it is a huge room like in your perfume example. If there is always a pressure, there is always a force. And since they are unquestionably exerting some force on the walls of its "container", they must be exerting force on each other as well. This simply occurs during the collisions where momentum is transferred. You don't need a pressure *difference* just pressure (which you have). My analogy to a highly pressurized canister was used simply to "see" that there must be some force. Decrease the pressure by making the "canister" a large room doesn't change the fundamental idea, it just means there is less pressure and less force acting between the molecules.

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I don't see how the gas does work as it is not expanding against an applied force.

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There IS an applied force though! When those molecules are redistributing around the room, they are constantly being bumped into by the other air molecules in the room, whatever they may be. Even if you imagine the rest of the room as a vacuum, the molecules must move in a *net* direction to get from their tiny little space after being squirted out of the perfume bottle to the rest of the room. If they stayed put (their "natural" state) they would simply be vibrating in place (like they were in the canister or bottle) and you could say there is zero net force. However, when they are put out in the open, the momentum transfer between the molecules causes a net motion towards the unoccupied regions of the room. Remember, Newton's original formulation of his first law was F = dp/dt (p is momentum), so since we are clearly changing the momentum of the molecules as they are going from being stationary (vibrating in place means no net motion and it can thus be considered stationary) to moving across the room -- there must be a force.

For the expansion of a gas, Work = (integral) p dV , where you are integrating from the initial volume the gas occupies to the final volume. This follows directly from the definition of work = F.ds (I could show you the derivation if you like). The point is that ANYTIME a gas goes from a region of smaller volume to larger in the real world, it is doing work and therefore there must be some force. As I said above, there will always be some pressure exerted. And in your perfume example, the molecules are doing work on each other (and the other molecules in the room), as it redistributes throughout the room when its volume is expanding. Work is also equal to kinetic energy change, and when the molecules go from being stationary in the bottle to having a definite non-zero net direction, there must be a kinetic energy change, which means there is work done, and to do work you must apply a force.

[Copernicus]

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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.

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While the bolded statement may seem obvious to you, it is not correct. The force of pressure is always perpindicular to the walls of the container. There is no net pressure exerted on "other molecules"

[Copernicus]

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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.


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The "blatant removeal of force" was intentional, because as Dr. Wong points out, those forces (or addition of energy to the system as I redescribed it) occurs BEFORE arriving at the state of the system being discussed. Once the system is in that state NO ADDITIONAL FORCE IS NECCESSARY. That is what the ChrisV means by diffusion not being CAUSED BY A FORCE.

[uDevil]

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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.

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So we can set up situations in which forces are acting and not acting, while diffusion occurs anyway. This shows those forces do not cause diffusion.

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If it's not, then sorry for interrupting your lively thread. [img]/images/graemlins/smile.gif[/img]

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Apparently the key is to ask a crappy question. It seems to be coming down to definitions. Have we had the "what is a 'cause'" thread yet?

[Chips_]

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So we can set up situations in which forces are acting and not acting, while diffusion occurs anyway. This shows those forces do not cause diffusion.

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Yes correct. Good observation. And as you mentioned about the question - sometimes the end result of an investigation leads us back to the question again. We come up with a better way of asking the question. If you want to ask "What causes diffusion" it's the Second Law of Thermodynamics as I mentioned earlier and as you confirmed in the online encyclopedia.

In physics problems sometimes most of the problem is figuring out where to start in terms of describing it. It can be a pain in the butt to know where to start. Some problems are best described in terms of forces. Others classes of problems are best described in terms of the law of conservation of momentum for example.

This problem that you have stated is best described by the Second Law of Thermodynamics which states that in a closed system there is a tendancy over time to move from order to disorder. That's all there is to this really. As the particles bang around they distribute themselves randomly throughout the room. Its the statistical tendancy of things that start out ordered to move to a disordered state that really "causes" diffusion of the perfume in the case that you have given. The Second law of Thermodynamics is the starting point for explaining a great many things. There are a whole categories of problems which draw on this Law as the "cause" behind the problem. I used to do short reviews for the MCAT (test for med school) and the MCAT test questions often have the second law of thermodynamics as correct choice as to the reason why something is happening. It fits into biological processes a lot.

Best of luck