The force on the walls of a vessel of a contained gas is due to

Options

A. repulsive force between gas molecules.
B. slight loss in average speed of a gas molecule after collision with wall.
C. change in momentum of a gas molecule due to collision with wall.
D. elastic collisions between gas molecules.

Answer

To answer the question about the force on the walls of a vessel containing gas, we can break down the explanation into clear steps:

### Step-by-Step Solution:

1. **Understanding Gas Molecules**:
- Gas molecules are in constant random motion. They have velocities that vary in direction and magnitude.

2. **Collision with the Wall**:
- When gas molecules collide with the walls of the container, they exert a force on the wall. This force arises from the change in momentum of the molecules.

3. **Elastic Collisions**:
- The collisions between gas molecules and the walls are considered elastic. This means that the total kinetic energy and momentum are conserved during the collision.

4. **Change in Momentum**:
- For a single gas molecule, when it strikes the wall, it has an initial velocity (let's denote it as \(v_1\)) and after the collision, it reverses direction with the same speed (denote this as \(v_2\)). Thus, if the molecule moves towards the wall with velocity \(v\), after the collision, it moves away with velocity \(-v\).
- The change in momentum (\(\Delta p\)) for one molecule can be calculated as:
\[ \Delta p = m(v_2 - v_1) = m(-v - v) = -2mv \]
- Here, \(m\) is the mass of the molecule.

5. **Force Calculation**:
- The force exerted on the wall due to the collision of gas molecules is defined as the rate of change of momentum. If we consider \(N\) molecules striking the wall per unit time, the total force \(F\) on the wall can be expressed as:
\[ F = N \cdot \Delta p / \Delta t \]
- Since pressure \(P\) is defined as force per unit area, we can relate this to the pressure exerted by the gas on the walls.

6. **Conclusion**:
- The force on the walls of the vessel is due to the change in momentum of gas molecules as they collide with the wall. Thus, the correct answer to the question is that the force is due to the change in momentum of gas molecules due to collision with the wall.

### Final Answer:
The force on the walls of a vessel containing gas is due to the change in momentum of gas molecules resulting from their collisions with the wall.

---