When a gas is heated in a vessel of constant volume , the pressure increases because

Options

A. The average force per impact of a molecule on a wall of the vessel increases
B. Molecules hit the walls more frequently
C. Molecules collide with each other more frequently
D. The number of molecules per unit volume of the gas increases

Answer

To solve the question, "When a gas is heated in a vessel of constant volume, the pressure increases because," we can break down the reasoning into clear steps.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a gas contained in a vessel with a constant volume. This means that the volume of the gas cannot change regardless of the temperature.

2. **Heating the Gas**:
- When the gas is heated, its temperature increases. According to the kinetic theory of gases, temperature is directly related to the average kinetic energy of the gas molecules.

3. **Increase in Kinetic Energy**:
- As the temperature rises, the kinetic energy of the gas molecules also increases. This means that the molecules move faster and have more energy.

4. **Molecular Collisions**:
- The gas molecules are in constant motion and collide with the walls of the vessel. With increased kinetic energy, these molecules collide with the walls more frequently and with greater force.

5. **Pressure Definition**:
- Pressure is defined as the force exerted per unit area. Since the force exerted by the molecules on the walls increases due to their higher speed and energy, the pressure inside the vessel must also increase.

6. **Conclusion**:
- Therefore, the increase in pressure when a gas is heated in a vessel of constant volume is due to the increase in the average force per impact of the gas molecules on the walls of the vessel, which is a direct result of the increase in their kinetic energy.

### Final Answer:
The pressure increases because the average force per impact of a molecule on the wall of a vessel increases due to the increase in kinetic energy of the gas molecules when heated.