Let's break down the question by applying the principles of gas behavior in a sealed container:
1. Understand the Relationship Between Temperature, Kinetic Energy, and Pressure:
- Temperature and Kinetic Energy:
In a sealed container of gas, temperature is directly related to the average kinetic energy of the gas particles. When the temperature increases, the kinetic energy of the gas particles also increases. This means that the gas particles move faster.
- Pressure:
Pressure ([tex]\(P\)[/tex]) is the force ([tex]\(F\)[/tex]) exerted by the gas particles per unit area ([tex]\(A\)[/tex]) on the walls of the container, given by the formula [tex]\(P = \frac{F}{A}\)[/tex].
2. Effects of Increased Temperature:
- Force of Collisions:
With increased temperature, particles move faster and collide with the container walls more frequently and with greater force.
- Area of Collisions:
In a sealed container with constant volume, the area ([tex]\(A\)[/tex]) over which particles collide remains the same.
3. Analyzing Each Option:
- Option A: "The change in temperature increases the area over which collisions of the container and gas particles occur, so the pressure decreases."
This is incorrect because the area of the container does not change with temperature in a sealed container with constant volume.
- Option B: "The change in temperature decreases the force of the collisions of the container and gas particles, so the pressure decreases."
This is incorrect because increasing the temperature increases the kinetic energy, thereby increasing the force of collisions, not decreasing it.
- Option C: "The change in temperature decreases the area over which collisions of the container and gas particles occur, so the pressure increases."
This is incorrect because the area over which collisions occur remains constant in a sealed container with no change in volume, and temperature does not affect this area.
- Option D: "The change in temperature increases the force of the collisions of the container and gas particles, so the pressure increases."
This is correct because an increase in temperature causes particles to move faster, increasing their kinetic energy. This results in more frequent and more forceful collisions with the container walls, thereby increasing the pressure.
Therefore, the correct choice is:
D. The change in temperature increases the force of the collisions of the container and gas particles, so the pressure increases.
