Momentum Conservation in Ideal Gas & Piston Collision

[qazxsw11111]

Homework Statement

The cylinder and piston are made of a thermal insulator. An atom of a gas collides with the piston at an angle and bounces off at an angle. State with a reason whether momentum of the atom is conserved in this collision.

Homework Equations

The Attempt at a Solution

I think that momentum of atom is not conserved as it is a vector quantity and hence change in momentum when there is a change in direction of the atom velocity.

However, the answer says that it is how you consider what is the "system". If atom is the "system", momentum is changed. If "piston+cylinder+atom"=system, momentum is conserved.

Im really confused! Which one is right?

 

[alphysicist]

Hi qazxsw11111,

Homework Statement

The cylinder and piston are made of a thermal insulator. An atom of a gas collides with the piston at an angle and bounces off at an angle. State with a reason whether momentum of the atom is conserved in this collision.

Homework Equations

The Attempt at a Solution

I think that momentum of atom is not conserved as it is a vector quantity and hence change in momentum when there is a change in direction of the atom velocity.

However, the answer says that it is how you consider what is the "system". If atom is the "system", momentum is changed. If "piston+cylinder+atom"=system, momentum is conserved.

Im really confused! Which one is right?

I'm not sure what you are asking here; you have the same answer as the answer key. The momentum of the atom changes.

If you are examining just the atom by itself (which is what is meant by defining the system to be the atom), then during the collision there is a large external impulse on the system--from the piston. With a large external impulse, the momentum changes (is not conserved).

If your system is (piston+cylinder+atom), then there is no external impulse due to the collision, because the collision forces are between system objects (and so action-reaction forces will have cancelling impulses). So for that system momentum is conserved.

Remember that the test for conservation of momentum is the impulse momentum relationship, which for average forces is:

$$\vec F_{\rm ext}\Delta t=\Delta \vec p$$

(and there is also the integral form if your problem requires it).

 

[baba89]

I would say that both answers are correct. It ultimately depends on how you define the system and what external forces are acting on it.

If we consider just the atom as the system, then the momentum would not be conserved as it changes direction after colliding with the piston. However, if we consider the entire system of the piston, cylinder, and atom, then the momentum would be conserved as there are no external forces acting on the system.

Additionally, it is important to note that in an ideal gas, the collisions between gas particles and the walls of the container are elastic, meaning that there is no loss of kinetic energy in the collision. This allows for the conservation of both momentum and energy in the system.

In conclusion, both answers are valid and it is important to carefully define the system and consider external forces when analyzing the conservation of momentum in a collision.