Question

The elastic collision should be satisfying 1. (kinetic) energy conservation and 2. momentum conservation.

Lets saying the wall is on x=Lx, and the x-dir velocity of a molecule is vx. The textbook and other sources that I saw, after the collision, the velocity of a molecule changing from vx to −vx. It is obvious after the collision, the kinetic energy of a molecule is the same and it is reasonable because in thermal equilibrium the internal energy of a system must be not changed (and a molecule belongs to the system). But the momentum obviously changed (mvx to −mvx). Why this collision is elastic? Should I consider the wall also as included in a system?

Answer 1

The collision between a gas molecule and a wall is an elastic collision that satisfies both energy conservation and momentum conservation. The velocity and kinetic energy of the gas molecule remain the same after the collision, while the momentum changes. The wall should be included as part of the system to ensure both energy and momentum conservation.

Step-by-step explanation:

The collision between a gas molecule and a wall is an elastic collision that satisfies both energy conservation and momentum conservation. In an elastic collision, the total kinetic energy of the system remains constant before and after the collision. This means that the velocity and kinetic energy of the gas molecule will remain the same after the collision. However, the momentum of the system does change, as the momentum of the molecule changes from mvx to -mvx.

In this case, the wall can be considered as part of the system. The collision with the wall causes a change in the momentum of the gas molecule, and the wall exerts an equal and opposite force on the molecule, satisfying Newton's third law of motion. So, to ensure both energy and momentum conservation, it is important to include the wall as part of the system.