Answer :
To understand the effect of an increase in temperature on a sealed container of gas with no change in volume, we need to analyze how temperature affects the behavior of gas molecules and, consequently, the pressure within the container.
1. Temperature and Kinetic Energy:
- Temperature is directly related to the kinetic energy of gas particles. When the temperature of a gas increases, the kinetic energy of its molecules also increases. This means that the gas molecules move faster and collide with more force.
2. Pressure and Collisions:
- Pressure within a container is the result of gas molecules colliding with the walls of the container. The more forceful the collisions, the higher the pressure. Pressure is given by the formula [tex]\( P = \frac{F}{A} \)[/tex], where [tex]\( F \)[/tex] is the force of the collisions and [tex]\( A \)[/tex] is the area of the walls.
3. Effect of Volume:
- In this scenario, the volume of the container does not change. Since the volume is constant, the area [tex]\( A \)[/tex] over which the force is exerted also remains constant.
Given these points, let's analyze each option provided:
- Option A: The change in temperature increases the force of the collisions of the container and gas particles, so the pressure increases.
- This statement is consistent with our understanding. An increase in temperature increases the kinetic energy of gas particles, leading to more forceful collisions. Since the volume (and hence the area [tex]\( A \)[/tex]) remains unchanged, the increased force [tex]\( F \)[/tex] results in increased pressure [tex]\( P \)[/tex].
- Option B: The change in temperature increases the area over which collisions of the container and gas particles occur, so the pressure decreases.
- This statement is incorrect because the volume of the container is constant, meaning the area over which collisions occur does not change. There is no increase in area, so this option can be ruled out.
- Option C: The change in temperature decreases the force of the collisions of the container and gas particles, so the pressure decreases.
- This statement is incorrect. An increase in temperature actually increases the force of collisions, not decreases it.
- Option D: The change in temperature decreases the area over which collisions of the container and gas particles occur, so the pressure increases.
- This statement is also incorrect because the area does not decrease with an increase in temperature when the volume is constant.
Given this analysis, the correct answer is:
A. The change in temperature increases the force of the collisions of the container and gas particles, so the pressure increases.
1. Temperature and Kinetic Energy:
- Temperature is directly related to the kinetic energy of gas particles. When the temperature of a gas increases, the kinetic energy of its molecules also increases. This means that the gas molecules move faster and collide with more force.
2. Pressure and Collisions:
- Pressure within a container is the result of gas molecules colliding with the walls of the container. The more forceful the collisions, the higher the pressure. Pressure is given by the formula [tex]\( P = \frac{F}{A} \)[/tex], where [tex]\( F \)[/tex] is the force of the collisions and [tex]\( A \)[/tex] is the area of the walls.
3. Effect of Volume:
- In this scenario, the volume of the container does not change. Since the volume is constant, the area [tex]\( A \)[/tex] over which the force is exerted also remains constant.
Given these points, let's analyze each option provided:
- Option A: The change in temperature increases the force of the collisions of the container and gas particles, so the pressure increases.
- This statement is consistent with our understanding. An increase in temperature increases the kinetic energy of gas particles, leading to more forceful collisions. Since the volume (and hence the area [tex]\( A \)[/tex]) remains unchanged, the increased force [tex]\( F \)[/tex] results in increased pressure [tex]\( P \)[/tex].
- Option B: The change in temperature increases the area over which collisions of the container and gas particles occur, so the pressure decreases.
- This statement is incorrect because the volume of the container is constant, meaning the area over which collisions occur does not change. There is no increase in area, so this option can be ruled out.
- Option C: The change in temperature decreases the force of the collisions of the container and gas particles, so the pressure decreases.
- This statement is incorrect. An increase in temperature actually increases the force of collisions, not decreases it.
- Option D: The change in temperature decreases the area over which collisions of the container and gas particles occur, so the pressure increases.
- This statement is also incorrect because the area does not decrease with an increase in temperature when the volume is constant.
Given this analysis, the correct answer is:
A. The change in temperature increases the force of the collisions of the container and gas particles, so the pressure increases.
