# Boyant Force Questioni!^^ Again?

1. Aug 5, 2004

### HungryChemist

Boyant Force Questioni!^^ Again??

I already know that there were many posts relating to boyant force. The reason I know is because I read them all but still very confused so I need help from you guyz. T_T I am sorry for my bad English.

My problem is with the explanation that is most commonly given out for the question why hot air rise. For me it is hard to apply the concept of boyant force to the system which is the collection of particles with higher kinetic energy. Why? Imagine there is a container, half filled by hot air molecules. Now to work out this problem using newton's law with boyant force concept, I need to have well defined system. To define system as the collection of particles with higher kinetic energy, I realize that I can't really define the volume of my system cuz the particles will swirl around in the certain region of box, will diffuse, and as guessed, will rise up. With out definite volume I can not give any means to its density. So I am stuck. I begin to doubt the concept of boyant force and density difference is not really explaning the question without skipping large step. Can somebody help me to understand?

For all that is said, I have two specific question.

Imagine we have a cubic container composed of gas. Let's say that there are many many gas molecules with low temperature. If we place the same gas molecule(Only one of it!) but with greater kinetic energy and release it from the very bottom of the container, will that one gas molecule rise up?

My another question is this....

Imagine there is a cubic box. Box is half filled with gas with higher kinetic energy and half filled with lower kinetic energy. Initially hotter gas molecules and cold gas molecules are positioned through out the space proportionally. What I mean is....hmmmmm.....the density of number of molecules per volume of space is constant throught the region that is bounded by the cubic box. Now, do you think the gas molecules with higher kinetic energy will begin to rise???? (If so, isn'it violating the law's of thermodynamics?? decreasing the entropy???)

Excuse me if I am not so clear in terms and definitions.

Last edited: Aug 5, 2004
2. Aug 5, 2004

### Gonzolo

It has energy, and thus speed, so it will bounce off container walls. But not nessarily rise. It needs to be with lower energy molecules and gravity to rise. The low energy molecules don't take so much space, so they are denser, and thus heavier as a whole. The energetic ones go where there is room, upwards.

The energetic ones push away the cold ones, which fall (or "Plinko") to the ground. An energetic one bounces off higher in than a cold one. The cold ones who fall down don't bounce back up as much.

3. Aug 5, 2004

### HungryChemist

When you say something is denser than the other, I really get lost. How would you define a density of diffusing gas?

The one gas molecules with high kinetic energy is 'with' lower energy molecules which occupies most of the region of the cubic box. And sorry if didn't specifically mentioned, but the gravity is acting here too! So then, as you said the single molecule will go up???

'an energetic one bounces off higher in than a cold one' doesn't make me to understand why the energetic one should rise. Cuz I can argue that the energetic one can bounces back again and drops down in the box further than the cold one.

4. Aug 6, 2004

### Gonzolo

Density of a diffusing gas : $$\rho_{gas x}(x,y,z,t)$$ But we don't need that to understand, so let's forget it for now. I find it easier to understand imagining a gas as rubber balls anyway.

Having one hot molecule among many cold ones, yes, the hot one will rise. This is because when any cold one go down, it doesn't come up again as high as the hot one. If you wait long enough the end result would be a new "floor" of cold molecules with the hot one bouncing on top of them.

Imagine those pools of plastic balls for kids. Those are all "cold molecule". If one of them is shaking a lot for an imaginary reason, it will move around until after sometime, it will by pure chance go on top. Once it is there, it won't be able to go back down, because the cold balls will have formed a new "floor" underneath.

"Cuz I can argue that the energetic one can bounces back again and drops down in the box further than the cold one."

No you can't! There is a floor! Take a hundred balls boucing on the floor, half of which are more energetic (bounce higher) than the other. The average height of the energetic ones is greater! That's all! The energetic balls are statistically "risen" relative to the others.

5. Aug 6, 2004

### Clausius2

This is my version:

First question: If you have a box filled with air molecules at 200K and you add one molecule with a kinetic energy equivalent to 1000K , perhaps this molecule crash into others, slowing down his kinetic energy and creating certain number of molecules (certain mass) that would have instantaneously less average density than the sorrounding ones. The gravity forces would act over the molecules above them. But I think that this effect has no sense with such small perturbation. Perhaps times involved in energy dissipation are much smaller than those involved in the macroscopic mass movement (bouyancy forces or convection).

Second question: this is not violating any thermodynamic law. The movement of the air molecules is an unsteady proccess. Second law of thermodynamic is applied to each one fluid particle. I mean, the diffussing and convective proccess we are talking about is governed by the Navier-Stokes equations. Surely, each molecule transports certain amount of entropy to other box parts, due to convective inertia, heat transfer, and viscosity (Rayleigh) dissipation. But the total variation in time (integrated at all volume) would be increasing in each instant of time. As t--->infinite, you could apply the classical 2nd thermodynamic law. The gas will be reached the complete steady state, probably having a higher average temperature, and if the boundaries are adiabatic, the system entropy would be increased.

6. Aug 6, 2004

### BobG

No molecule is going to go very far. It will bump into another and some of the energetic molecule's energy gets transferred to the low energy molecule. Eventually, if it's a closed system, you reach equilibrium where all of the molecules have the same energy (and temperature). If the distribution were uniform throughout the box, the energy of the molecules would quickly stablize to a common level, as well.