Kinetic Theory of Temperature and Pressure
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AP Physics 2 › Kinetic Theory of Temperature and Pressure
A vacuum pump removes gas from a rigid container while the remaining particles keep the same average speed. Which statement best explains the pressure change?
The pressure is unchanged because pressure depends only on particle mass, which is unchanged for each particle.
The pressure decreases because fewer particles collide with the walls per unit time.
The pressure increases because removing particles increases the average force of each collision.
The pressure is unchanged because temperature measures total energy, and total energy stays the same when particles are removed.
Explanation
This question tests understanding of kinetic theory of temperature and pressure. Pressure arises from particle collisions with container walls, depending on both collision frequency and momentum transfer per collision. When a vacuum pump removes particles while maintaining the same average speed (constant temperature), the number of wall collisions per unit time decreases proportionally. With fewer particles creating fewer collisions, the average force on walls decreases, reducing pressure. Choice C incorrectly claims pressure depends only on individual particle mass—pressure actually depends on the total collision rate, which scales with particle number. When analyzing particle removal at constant temperature, remember that pressure is proportional to particle density (number per volume).
Two samples of the same gas have equal volumes and equal average particle speeds, but sample 2 has twice as many particles. Which statement best describes the pressure in sample 2?
It is lower because the same temperature is shared among more particles, reducing kinetic energy per particle.
It is the same because pressure depends only on particle speed, not on the number of particles.
It is higher because doubling the number of particles doubles each particle’s mass, increasing pressure.
It is higher because more particles produce more wall collisions per unit time at the same average speed.
Explanation
This question tests understanding of kinetic theory of temperature and pressure. Pressure results from particle collisions with container walls, depending on both the force per collision and the number of collisions per unit time. With equal average particle speeds, each collision transfers the same momentum, but sample 2 has twice as many particles creating twice as many wall collisions per second. Since pressure is force per unit area and force is proportional to collision rate, doubling the number of particles doubles the pressure. Choice A incorrectly suggests temperature is "shared" among particles—temperature depends only on average kinetic energy per particle, not particle count. When comparing gas samples, remember that pressure scales linearly with particle density at constant temperature.
In a rigid container, a gas reaches equilibrium after heating, and the average kinetic energy per particle increases. Compared to before heating, the temperature is
unchanged because temperature depends on the container size, which is constant.
lower because particles collide more often, which reduces their kinetic energy over time.
higher because temperature measures the total kinetic energy of all particles in the container.
higher because temperature is proportional to the average kinetic energy of the particles.
Explanation
This question tests understanding of kinetic theory of temperature and pressure. Temperature is defined as a measure proportional to the average kinetic energy of particles in a substance. When heating increases the average kinetic energy per particle, the temperature increases by definition—this is the fundamental connection between microscopic motion and macroscopic temperature. The rigid container ensures particle number remains constant, so the increase in average kinetic energy directly translates to higher temperature. Choice D incorrectly defines temperature as total kinetic energy, which would make temperature depend on the amount of substance rather than its thermal state. To determine temperature changes, always focus on average kinetic energy per particle: higher average KE means higher temperature.
A gas in a sealed rigid container is cooled so the average particle speed decreases. Which statement best explains the resulting pressure change?
The pressure is unchanged because pressure depends only on particle mass, which does not change.
The pressure decreases because particles transfer less momentum to the walls during collisions.
The pressure decreases because cooling increases the number of particles that hit the walls each second.
The pressure increases because particles slow down and therefore push on the walls for a longer time.
Explanation
This question tests understanding of kinetic theory of temperature and pressure. When gas is cooled, the average kinetic energy of particles decreases, meaning particles move more slowly. Slower particles have less momentum (p = mv), so each collision with the container walls transfers less momentum, creating smaller impulse forces. Additionally, slower particles take longer to travel between walls, reducing collision frequency. Both effects—weaker collisions and fewer collisions per unit time—combine to decrease the pressure on the container walls. Choice C incorrectly suggests slower particles increase pressure by lingering at walls—in reality, elastic collisions are instantaneous regardless of speed. To predict pressure changes, consider both collision strength (momentum transfer) and collision frequency.
A rigid container of ideal gas is heated briefly, then allowed to reach a new equilibrium. After heating, the average particle speed is higher, indicating greater average kinetic energy. The number of particles and the container volume remain constant. Which statement best explains why the final pressure is higher than the initial pressure?
The final pressure is lower because at higher temperature particles slow down between collisions.
The final pressure is higher because heating increases particle mass, which raises pressure automatically.
The final pressure is higher because particles move faster and increase momentum transfer to the walls per unit time.
The final pressure is unchanged because temperature measures the total energy, which stays constant in a rigid container.
Explanation
This question tests understanding of kinetic theory of temperature and pressure. After heating, particles have higher average speed and kinetic energy, indicating higher temperature. In the rigid container with constant volume and particle number, these faster particles collide with walls more frequently and with greater force per collision. Both effects increase the momentum transferred to walls per unit time, resulting in higher pressure at equilibrium. Choice C incorrectly claims temperature measures total energy and that this somehow keeps pressure constant, misunderstanding that temperature is average kinetic energy per particle. The fundamental relationship is: in a rigid container, pressure is directly proportional to temperature because faster particles create more forceful collisions.
Two rigid containers at the same temperature hold equal numbers of particles: one has helium, the other xenon. Which statement best compares their pressures?
The pressures are the same because equal temperature implies equal average kinetic energy, giving the same average collision impulse per particle for equal $N$ and $V$.
The xenon pressure is higher because heavier particles create more pressure regardless of speed.
The helium pressure is higher because lighter particles always move slower at the same temperature.
The pressures are the same because temperature measures the total kinetic energy, which is identical only when masses are equal.
Explanation
This question tests understanding of kinetic theory of temperature and pressure. At the same temperature, all ideal gas particles have the same average kinetic energy (½mv²), regardless of their mass. While helium atoms are lighter and thus move faster, and xenon atoms are heavier and move slower, the product of mass and velocity squared remains constant. Since pressure depends on momentum transfer (mass × velocity) and collision frequency, the lighter helium atoms moving faster create the same average impulse per collision as heavier xenon atoms moving slower. Choice A incorrectly assumes heavier particles automatically create more pressure, ignoring that lighter particles compensate with higher speeds. For ideal gases at equal temperature, pressure depends only on particle density (N/V), not particle type.
A gas in a rigid container is stirred with a paddle wheel, increasing average particle speed without changing particle number. Which statement best describes the temperature change?
The temperature increases because temperature measures the total kinetic energy of all particles, regardless of average speed.
The temperature decreases because faster particles lose energy more quickly in collisions.
The temperature increases because temperature corresponds to the average translational kinetic energy of the particles.
The temperature stays the same because temperature depends only on the container’s volume.
Explanation
This question tests understanding of kinetic theory of temperature and pressure. Stirring a gas with a paddle wheel adds mechanical energy to the system, increasing the average speed and thus the average kinetic energy of particles. Since temperature is defined as a measure of average translational kinetic energy per particle, increasing particle speeds directly increases temperature. This demonstrates how work done on a gas (mechanical stirring) converts to internal energy (particle motion). Choice D incorrectly focuses on total kinetic energy rather than average, missing that temperature is an intensive property independent of system size. When work is done on a gas, the added energy increases particle motion and thus temperature.
A rigid container of argon is cooled. Particle speeds decrease, so wall collisions become less frequent and less forceful. Which statement best explains the pressure change?
The pressure decreases because particles become more massive at lower temperature.
The pressure decreases because temperature measures the total energy, which must drop when pressure drops.
The pressure decreases because the container volume increases as particles slow down.
The pressure decreases because slower particles transfer less momentum per collision and collide less often with the walls.
Explanation
This question tests understanding of kinetic theory of temperature and pressure. When a gas is cooled, the average kinetic energy of particles decreases, causing them to move more slowly. These slower particles collide with container walls less frequently and with less force, transferring less momentum per collision. Since pressure results from the cumulative effect of these collisions, both reduced collision frequency and smaller momentum transfer lead to decreased pressure. Choice C incorrectly suggests that particle mass changes with temperature, confusing the relationship between kinetic energy and mass. Remember that pressure changes result from changes in particle motion: slower particles mean weaker and less frequent collisions.
A sealed container of gas is warmed so particle speeds rise. The container’s volume is constant, so wall collisions become more frequent and more forceful. Which statement best explains why temperature rises?
Temperature rises because pressure depends only on particle mass, which increases when heated.
Temperature rises because particles slow down at higher temperature, raising collision time.
Temperature rises because the particles’ average translational kinetic energy increases.
Temperature rises because the gas now contains more particles, increasing total energy.
Explanation
This question tests understanding of kinetic theory of temperature and pressure. Temperature is fundamentally a measure of the average translational kinetic energy of particles in the system. When a gas is warmed and particle speeds increase, the average kinetic energy (½mv²) increases proportionally. This direct relationship between particle kinetic energy and temperature explains why warming the gas raises its temperature. Choice C incorrectly states that particles slow down at higher temperature, which contradicts the basic principle that higher temperature means faster particle motion. Remember that temperature always reflects the average kinetic energy of individual particles, making it a microscopic property that manifests macroscopically.
A gas in a cylinder with a freely moving piston is slowly heated. Particles move faster and collide with the piston more frequently. Which statement best explains why the gas pressure stays approximately constant as it expands?
The pressure stays constant because temperature measures the total energy, which the piston removes.
The pressure stays constant because the piston moves outward, reducing collision frequency per area.
The pressure stays constant because increasing particle mass offsets the increased collision rate.
The pressure stays constant because higher temperature makes particles slow down between collisions.
Explanation
This question tests understanding of kinetic theory of temperature and pressure. When a gas is heated in a cylinder with a freely moving piston, particles gain kinetic energy and would normally increase pressure through more frequent and forceful collisions. However, the piston moves outward in response, increasing the volume and thereby increasing the distance between particles and walls. This expansion reduces the collision frequency per unit area back to its original value, maintaining constant pressure. Choice C incorrectly suggests particles slow down at higher temperature, which contradicts the fundamental principle that temperature correlates with particle speed. The strategy here is to recognize that a freely moving piston adjusts volume to maintain pressure equilibrium.