Equipartition Theory: Need Help with Gas Problem

[physicsCU]

Equipartition Theory

I need some help with a gas problem concerning statements about this theory.

Here are the statements: (we have to decide if they are true or false)

1. The Equipartition Theorem implies that \avg{v_x^2}=\avg{v_y^2}.
2. \avg{v_x^2}=\avg{v_y^2} owing to inelastic collisions between the gas molecules.
3. With just one particle in the container, the pressure on the wall (at x = L_x) is independent of L_y and L_z.
4. With just one particle in the container, the average force exerted on the particle by the wall (at x = L_x) is independent of L_y and L_z.

I guessed t,f,t,t. That was wrong.

I have no idea about this, my book doesn't cover it, not lectured on.

Can anyone help me?

 

[OlderDan]

I need some help with a gas problem concerning statements about this theory.

Here are the statements: (we have to decide if they are true or false)

1. The Equipartition Theorem implies that \avg{v_x^2}=\avg{v_y^2}.
2. \avg{v_x^2}=\avg{v_y^2} owing to inelastic collisions between the gas molecules.
3. With just one particle in the container, the pressure on the wall (at x = L_x) is independent of L_y and L_z.
4. With just one particle in the container, the average force exerted on the particle by the wall (at x = L_x) is independent of L_y and L_z.

I guessed t,f,t,t. That was wrong.

I have no idea about this, my book doesn't cover it, not lectured on.

Can anyone help me?

Are you saying all your answers are wrong? What is L? Is it dimensions of the box?

 

[physicsCU]

Well, it is mastering physics, it doesn't tell me if any are right, but if even one is wrong, i get counted as wrong.

L is the box's dimensions.

http://session.masteringphysics.com/problemAsset/1011124/12/SIG_pg_0.jpg

That is the image associated with this problem.

 

[OlderDan]

Deleted erroneous response


1 is true, all three directions have the same average

2 is false. The collisions are elastic

 

[physicsCU]

3 and 4 are false. The time it takes the particle to get back to any wall increases as the box size increases. The average time between collisions affects the average force on the walls.

1 is true, all three directions have the same average

2 is false. The collisions are elastic

Hmm, that didn't seem to do it. I know 1 is true and 2 is false, but i guess either three or four is true. Are you sure both are false?

 

[OlderDan]

Hmm, that didn't seem to do it. I know 1 is true and 2 is false, but i guess either three or four is true. Are you sure both are false?

Sorry. I had not seen the diagram before I replied earlier and had misinterpreted something. The x-component of the particles velocity will be constant, so it will hit the walls that limit the x range with the same frequency regardless of the other dimensions. The average force will be constant. However, the other dimensions determine the area of the walls that limit the x range, so they do affect the pressure.

 

[physicsCU]

No problem. Here is another one I am having trouble with though.

Another true/false.

If you heat a fixed quantity of gas, which of the following statements are true?

1. The volume will always increase.
2. If the pressure is held constant, the volume will increase.
3. The product of volume and pressure will increase.
4. The density of the gas will increase.
5. The quantity of gas will increase.

I guessed f,t,f,f,f. But I think the first one is true, and the others are what I think they are. Can you confirm this?

 

[OlderDan]

No problem. Here is another one I am having trouble with though.

Another true/false.

If you heat a fixed quantity of gas, which of the following statements are true?

1. The volume will always increase.
2. If the pressure is held constant, the volume will increase.
3. The product of volume and pressure will increase.
4. The density of the gas will increase.
5. The quantity of gas will increase.

I guessed f,t,f,f,f. But I think the first one is true, and the others are what I think they are. Can you confirm this?

The ideal gas law is PV = nRT

n and R are both constant in this problem. n is "the quantity of gas" expressed appropriately. If the temperature is increased, the product PV will increase, so 3 is true. From that it follows that 2 is true, as you said