What is the force acting on a particle during a change in temperature?

[Lucw]

Hello.

Galileo claimed that a body could not "by itself" change the state of rest or uniform rectilinear motion of its center of gravity.
Newton clarified this with the notion of force and inertia. F = m.a.
So let's follow a mass m.

Either a closed container containing a gas. And one of the mass gas particles m .
The temperature is T. And the pressure in the tank is P. The average speed of the gas particles is therefore V.
And the average speed of our particle of mass m is thus also V.
The temperature is increased by 100 °.
The pressure increases. And the average speed of the gas particles has therefore increased.
And the average velocity of our particle of mass m has thus also increased.
F = m.a.
What force has acted on our particle during the rise in temperature?
I think it's a good question.

Have a good day.

Lucw

 

[andrewkirk]

What force has acted on our particle during the rise in temperature?

The force will be related to whatever it was that made the temperature rise. For instance Joule, in his original experiments, used a motor-driven paddle in a vat of liquid that stirred the liquid and thereby made its temperature rise. In this case, I imagine the gas is heated by heating the walls of the container. That means the walls vibrate faster and hence push harder on molecules that bounce off them.

 

[Lucw]

Thank you for your reply.

You say:
"That means the walls vibrate faster and hence push harder on molecules that bounce off them"

Let say the molecules of the walls vibrate faster.
But we have as much chance of the gas particle arriving when the molecule of the wall recedes - the speed of the gas particle decreases - than when the molecule of the wall advances (towards the particle of gas) - the speed of the gas particle increases -.
Is there another explanation?

Lucw

 

[andrewkirk]

we have as much chance of the gas particle arriving when the molecule of the wall recedes - the speed of the gas particle decreases - than when the molecule of the wall advances (towards the particle of gas) - the speed of the gas particle increases

Yes but the deficiency in energy from a collision when the wall is receding will be less than the excess of energy when it is advancing, because KE is a nonlinear (convex) function of velocity. The net effect will be an increase in average particle KE (Jensen's inequality).

There will be other effects as well, such as radiation inwards from the walls. Some of that radiation will be absorbed by particles, increasing their momentum and energy. You can think of an increase in momentum from the absorption of a photon as the application of a force.

 

[jbriggs444]

But we have as much chance of the gas particle arriving when the molecule of the wall recedes - the speed of the gas particle decreases - than when the molecule of the wall advances (towards the particle of gas) - the speed of the gas particle increases

Are you sure about that claim? Think carefully.

If you are driving on a highway, is the number of cars you overtake per minute on average equal to the number that you pass going the opposite direction?

 

[Dale]

a body could not "by itself" change the state of rest or uniform rectilinear motion of its center of gravity.

Yes.

Either a closed container containing a gas. And one of the mass gas particles m .

Even if the closed container containing a gas is “by itself” the individual gas particles are not. A change in their average speed does not violate the above.

 

[Lucw]

Hello.

Thank you very much.
I have to think about your idea.
I like very much the note of Jbriqqs444. But the gas particule are not on the highway...
They come somtime near a wall made of garages. Where cars go out and in all the times...

And i also try to find application of Jensen's inequality.
Have you somes?

Have a nice day.
There is sun in my country. Long time ago we have not seen "him".
It is pleasant.

 

[Dale]

But we have as much chance of the gas particle arriving when the molecule of the wall recedes - the speed of the gas particle decreases - than when the molecule of the wall advances (towards the particle of gas) - the speed of the gas particle increases -.

You should think carefully about what @jbriggs444 said. He is correct. Not only are the chances not equal, they depend on the speed (for a similar reason as with the cars).

If the speed of the gas is low enough then the probability that it collides while the wall recedes is 0 and the probability that it collides while the wall advances is 1. As the speed increases the probabilities change.

 

[Lucw]

Hello Dale.

I am not consider the probability that the gas collides with the wall; it depends on the dimensions of the tank. If one of the dimensions of the tank is very very very small, the probability of collision with the wall is greater than with another gas particle. This has to do with the average free path of a particle of gas.
No no.
I consider the moment of the encounter between a particle of gas and a particle of the wall. But yes, if the velocity of the gas particle is low, it seems to me that it is more likely to encounter the gas particle when it comes to it.
As said @ jbriggs444

Lucw

 

[jbriggs444]

it seems to me that it is more likely to encounter the gas particle when it comes to it.
As said @ jbriggs444

That is not the comparison that I have in mind.

The collisions of gas molecules with each other are irrelevant. They conserve energy. Any energy added to the one molecule is energy subtracted from the other. One may as well ignore such collisions entirely. What you cannot ignore are collisions with the wall.

While the wall is vibrating away from the gas, it will have fewer than normal collisions with gas molecules. The gas molecules are trying to catch up with a receding wall. While the wall is vibrating toward the gas, it will have more than normal collisions with gas molecules. Not only will gas molecules hit the wall, the wall will also sweep through a volume where gas molecules might already exist. The wall may even catch up with a molecule that is already moving away from the wall.