Warm air goes up....reason on a microscopic scale?

[jbriggs444]

I don't think you know what you're saying.

I am saying that a single molecule does not have a pressure. A bunch of molecules do. A single photon does not have a pressure. A bunch of photons do.

Can you calculate the pressure which you believe is associated with a single molecule of nitrogen at 500 meters/second?

Edit: Note that your calculation will at least implicitly use a reference frame against which that 500 meters/second is determined. This means that your calculated pressure will be a property of a molecule of nitrogen in the context of a reference frame, not an intrinsic property of the molecule.

 

[NFuller]

my explanation is based on the idea that the system evolves towards the equilibrium. In other words, the hot gas goes up because that makes the system closer to the equilibrium.

I think your explanation is appropriate for a 'B' level thread, like this one. I was just pointing out that its difficult to justify the behavior of a dynamical system using results from equilibrium statistical mechanics. In your post #40, it looks like you are saying that the convection of the warm gas is driven by an increase in entropy. However, entropy is a rather useless variable for a non-equilibrium system and we aren't even guaranteed that the entropy is increasing as the gas flows upward. The only thing we do know is that when the gasses finally come to equilibrium, that will be a maximum entropy state.

 

[Zaya Bell]

I am saying that a single molecule does not have a pressure. A bunch of molecules do. A single photon does not have a pressure. A bunch of photons do.

Can you calculate the pressure which you believe is associated with a single molecule of nitrogen at 500 meters/second?

Edit: Note that your calculation will at least implicitly use a reference frame against which that 500 meters/second is determined. This means that your calculated pressure will be a property of a molecule of nitrogen in the context of a reference frame, not an intrinsic property of the molecule.

One molecule does have pressure. It's pressure is different from the macroscopic pressure of the gas which is the speed at which they strike the container and the area of movement. But rather, classically, as a result of their mass and acceleration. As much as one photon has energy and momentum it sure can exert pressure. If I shoot an electron, it also exert pressure on whatsoever it collides with. Generally, all particle exert pressure.

 

[jbriggs444]

One molecule does have pressure. It's pressure is different from the macroscopic pressure of the gas which is the speed at which they strike the container and the area of movement. But rather, classically, as a result of their mass and acceleration. As much as one photon has energy and momentum it sure can exert pressure. If I shoot an electron, it also exert pressure on whatsoever it collides with. Generally, all particle exert pressure.

That is not pressure. That is impulse. It is not an attribute of the molecule. It is an attribute of the interaction.

 

[hasahinivo]

Think of molecules as balls. Some are heavier, and some are lighter.

When 2 molecules collide, they interchange momentum and energy. Because energy and momentum is conserved, both molecules get similar amounts of momentum. I didn't said "the same momentum", because it depends on the relative speeds, but "similar momentum" is good enough to understand it. Here is a better explanation.

Because the lighter ball has less mass, it needs more speed for the same momentum, so the lighter ball gets more speed out of the collision (it also needs a lot more energy, because energy scales squared with speed).
Here are some illustrative video:





So, the lighter molecules run much faster after thermal equilibrium is achieved. Faster in all directions. If they were in zero gravity, the lighter molecules would escape faster in all directions, at the speed of sound.

In non zero gravity, molecules are bounded in all directions, except up, so they move up faster than the heavier molecules.
Going up requires more energy, because is necessary to fight against gravity, so not all molecules with the same weight go up. Only the ones with enough energy go up.

Because the lighter gas has more energy per molecule, it also has more molecules up.

 

[NFuller]

One molecule does have pressure. It's pressure is different from the macroscopic pressure of the gas which is the speed at which they strike the container and the area of movement. But rather, classically, as a result of their mass and acceleration. As much as one photon has energy and momentum it sure can exert pressure. If I shoot an electron, it also exert pressure on whatsoever it collides with. Generally, all particle exert pressure.

Pressure is an average macroscopic quantity of an entire system. I think you are envisioning a box with a single particle in it and saying that the walls of the box will experience some average pressure over long time scales as the particle bounces around inside. What @jbriggs444 is telling you is that the particle itself does not have pressure, rather only the walls of the box experience pressure.

Pressure is a property of the system not the particles alone. This is easy to see if you shrink the size of the box while keeping the temperature constant. The pressure will increase on the walls even though the molecules all still have the same kinetic energy.

 

[Demystifier]

However, entropy is a rather useless variable for a non-equilibrium system

I strongly disagree. Entropy is only useful when it changes, and it changes only in non-equilibrium.

 

[Brendan Graham]

Does that not beg the question? What do you mean by thermodynamic equilibrium for a single molecule within a container?

If one has a container at 100K and a molecule with a kinetic energy equivalent to 200K, is that molecule in thermodynamic equilibrium with the container? Is there enough information to tell?

 

[NFuller]

I strongly disagree. Entropy is only useful when it changes, and it changes only in non-equilibrium.

Entropy is a state variable only for systems at equilibrium. It is difficult to even define entropy for a dynamical system. Saying entropy is only useful for non-equilibrium systems strikes me as naive, since most texts on statistical mechanics and thermodynamics use entropy only when describing equilibrium states.

There have been attempts to define and use entropy for non-equilibrium systems, which have produced mixed results. Here's a short discussion on the subject https://arxiv.org/pdf/1305.3912.pdf.

 

[Demystifier]

Entropy is a state variable only for systems at equilibrium. It is difficult to even define entropy for a dynamical system. Saying entropy is only useful for non-equilibrium systems strikes me as naive, since most texts on statistical mechanics and thermodynamics use entropy only when describing equilibrium states.

Nonsense. Every thorough statistical mechanics textbook introduces Boltzmann and Gibbs entropy in some of the initial chapters, before even mentioning the concept of equilibrium.

Even you in your insight article https://www.physicsforums.com/insights/statistical-mechanics-part-equilibrium-systems/ have introduced Gibbs entropy before mentioning equilibrium and canonical ensemble.

My coworkers and me have been calculating entropy far from equilibrium in a dynamical system in this work: https://arxiv.org/abs/1011.4173v5

There have been attempts to define and use entropy for non-equilibrium systems, which have produced mixed results. Here's a short discussion on the subject https://arxiv.org/pdf/1305.3912.pdf.

In this paper authors require entropy to satisfy some additional properties. The standard Boltzmann and Gibbs entropy (which turn out to be equal only in equilibrium) do not need to satisfy all these properties.

 

[NFuller]

Every thorough statistical mechanics textbook introduces Boltzmann and Gibbs entropy in some of the initial chapters, before even mentioning the concept of equilibrium.

Even you in your insight article https://www.physicsforums.com/insights/statistical-mechanics-part-equilibrium-systems/ have introduced Gibbs entropy before mentioning equilibrium and canonical ensemble.

Right, but I can't use it to solve for the state of a system until I impose the equilibrium requirement. Even in Zwanzig's book on non-equilibrium systems, I don't think the word entropy even appears in the book; it's not shown in the glossary/appendix.

In this paper authors require entropy to satisfy some additional properties. The standard Boltzmann and Gibbs entropy (which turn out to be equal only in equilibrium) do not need to satisfy all these properties.

I'm not sure about this. I think if the entropy doesn't satisfy these properties, it isn't useful for determining the state of a system. Anyways, I will read through your paper to get a better understanding of your view. I think we are deviating from the intention of this thread.

 

[Demystifier]

Right, but I can't use it to solve for the state of a system until I impose the equilibrium requirement. Even in Zwanzig's book on non-equilibrium systems, I don't think the word entropy even appears in the book; it's not shown in the glossary/appendix.

I'm not sure about this. I think if the entropy doesn't satisfy these properties, it isn't useful for determining the state of a system. Anyways, I will read through your paper to get a better understanding of your view. I think we are deviating from the intention of this thread.

I agree that out of equilibrium, entropy is less useful to describe the state. Nevertheless it can be defined any may be very useful for studying the second law.