- A sample of ideal gas is compressed quickly in an insulated cylinder, decreasing volume so particles hit the walls more often. Which statement best explains the temperature change of the gas?
Answer: The temperature increases because work done on the gas increases average particle kinetic energy.
This question tests understanding of kinetic theory of temperature and pressure. During rapid compression of an insulated gas, the moving piston does work on the gas particles by colliding with them as it moves inward. These collisions transfer energy to the particles, increasing their average kinetic energy and thus their average speed. Since temperature is proportional to average particle kinetic energy, the temperature increases. Choice A incorrectly suggests that collisions remove energy, when actually the piston adds energy to particles during compression. Remember that in adiabatic compression (no heat exchange), work done on the gas converts directly to increased particle kinetic energy and temperature.
- A gas in a rigid container is heated until the average particle kinetic energy doubles. Particle collisions with the walls become more frequent and involve larger momentum changes. Which statement best explains the pressure change?
Answer: Pressure increases because larger average kinetic energy leads to greater momentum transfer in collisions.
This question tests understanding of kinetic theory of temperature and pressure. When average particle kinetic energy doubles, particles move faster (speed increases by √2 since KE ∝ v²), leading to more frequent wall collisions and greater momentum transfer per collision. The pressure, which depends on the rate of momentum transfer to walls, increases as a result of both effects. Since temperature is proportional to average kinetic energy, doubling the kinetic energy doubles the temperature, and for an ideal gas in a rigid container, this doubles the pressure. Choice D incorrectly claims particles move slower at higher temperature, contradicting fundamental kinetic theory. The strategy is to connect microscopic changes (particle energy) to macroscopic observables (pressure) through collision dynamics.
- 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?
Answer: The pressure decreases because slower particles transfer less momentum per collision and collide less often with the walls.
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 rigid container of gas is cooled until particles move more slowly. Which statement best explains why the pressure decreases?
Answer: The pressure decreases because slower particles collide less often and with smaller momentum change at the walls.
This question tests understanding of kinetic theory of temperature and pressure. Cooling a gas reduces the average kinetic energy of particles, causing them to move more slowly. These slower particles collide with container walls less frequently because they take longer to traverse the container. Additionally, each collision involves less momentum transfer since momentum equals mass times velocity. The combination of reduced collision frequency and smaller momentum change per collision results in decreased pressure on the walls. Choice C incorrectly claims particles move faster at lower temperature, directly contradicting the fundamental temperature-kinetic energy relationship. Remember that cooling always reduces particle motion, leading to weaker and less frequent collisions.
- Two sealed rigid flasks contain equal amounts of gas. Flask B has twice as many particles as flask A, and particles have the same average kinetic energy in both. Compared to flask A, the pressure in flask B is
Answer: greater because more particles cause more collisions per unit time with the walls.
This question tests understanding of kinetic theory of temperature and pressure. Pressure results from particle collisions with container walls, depending on both the number of particles and their average kinetic energy. Since flask B has twice as many particles with the same average kinetic energy (same temperature), it experiences twice as many collisions per unit time with the walls. Each collision transfers the same average momentum as in flask A, so the total momentum transfer rate doubles, doubling the pressure. Choice C incorrectly assumes that more particles must share a fixed total energy, but the problem states particles have the same average kinetic energy. The key principle is that pressure is proportional to particle density when temperature is constant.
- Two rigid containers at the same temperature hold equal numbers of particles: one has helium, the other xenon. Which statement best compares their pressures?
Answer: 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.
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. - 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
Answer: higher because temperature is proportional to the average kinetic energy of the particles.
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 sealed rigid container holds a dilute gas. A heater is turned on, and particles move faster, striking the walls more often and with greater momentum change. Which statement best explains the change in pressure?
Answer: The pressure increases because faster particles cause more frequent, harder collisions with the walls.
This question tests understanding of kinetic theory of temperature and pressure. In kinetic theory, gas pressure results from particles colliding with container walls, transferring momentum during each collision. When temperature increases, particles move faster on average, leading to both more frequent collisions and greater momentum transfer per collision. This dual effect causes pressure to increase in a sealed container. Choice B incorrectly confuses temperature with total internal energy rather than average kinetic energy per particle. The key strategy is to remember that pressure depends on both collision frequency and momentum change per collision, both of which increase with particle speed.
- Two identical boxes contain the same number of helium atoms. In box 1, atoms have higher average speed. Compared to box 2, box 1's temperature is
Answer: higher because temperature is proportional to the average translational kinetic energy per atom.
This question tests understanding of kinetic theory of temperature and pressure. Temperature is a measure of the average translational kinetic energy per particle in a system, not the total energy or number of particles. Since box 1 contains atoms with higher average speed, and kinetic energy equals ½mv², these atoms have greater average kinetic energy. For ideal gases, temperature is directly proportional to this average kinetic energy, making box 1's temperature higher than box 2's. Choice D incorrectly states that temperature measures total kinetic energy rather than average—a misconception that would make temperature depend on the number of particles present. To determine temperature relationships, always focus on average kinetic energy per particle, not total energy.
- 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?
Answer: The pressure decreases because fewer particles collide with the walls per unit time.
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).
- 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?
Answer: The final pressure is higher because particles move faster and increase momentum transfer to the walls per unit time.
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 identical rigid containers hold the same gas; in container 2 the average particle speed is higher. Compared to container 1, the temperature in container 2 is
Answer: higher because temperature is proportional to the average kinetic energy of the particles.
This question tests understanding of kinetic theory of temperature and pressure. Temperature is a measure of the average kinetic energy of particles in a substance, not the total kinetic energy of all particles. Since container 2 has higher average particle speed, and kinetic energy equals ½mv², the average kinetic energy per particle is higher in container 2. This directly means container 2 has a higher temperature, as temperature is proportional to average kinetic energy. Choice B incorrectly states that temperature equals total kinetic energy—this would make temperature depend on the number of particles, which is wrong. To determine temperature relationships, always focus on average kinetic energy per particle, not total energy or individual collision properties.
- In a rigid container, the number of gas particles is doubled by adding more of the same gas while temperature stays the same. Which statement best explains the pressure change?
Answer: The pressure increases because more particles cause more wall collisions per unit time at the same average kinetic energy.
This question tests understanding of kinetic theory of temperature and pressure. When more particles are added to a rigid container at constant temperature, each particle maintains the same average kinetic energy and speed. However, doubling the number of particles doubles the total number of wall collisions occurring per unit time. Since pressure results from the cumulative momentum transfer from all collisions, twice as many particles create twice the pressure, even though individual collision characteristics remain unchanged. Choice C incorrectly suggests that adding particles makes each one move slower, confusing particle density with individual particle behavior. At constant temperature and volume, pressure is directly proportional to the number of particles present.
- A gas is in a rigid container. The average speed of the particles increases while the number of particles and volume stay constant. Which statement best explains how temperature changes?
Answer: Temperature increases because average translational kinetic energy increases with particle speed.
This question tests understanding of kinetic theory of temperature and pressure. Temperature is defined as a measure of the average translational kinetic energy of particles in a system. When particle speed increases while mass remains constant, the kinetic energy (½mv²) increases proportionally to the square of the speed. This increase in average kinetic energy directly corresponds to an increase in temperature. Choice D incorrectly identifies temperature as total kinetic energy rather than average kinetic energy per particle. Always remember that temperature reflects the average energy of individual particles, not the collective energy of all particles combined.
- 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?
Answer: Temperature rises because the particles' average translational kinetic energy increases.
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.
- In a rigid container, some gas particles are replaced with the same number of lighter particles, with the same average kinetic energy per particle. Which statement best describes the pressure?
Answer: The pressure increases because lighter particles have greater average speed at the same kinetic energy, increasing collision rate.
This question tests understanding of kinetic theory of temperature and pressure. When lighter particles have the same average kinetic energy as heavier particles, they must move faster because KE = ½mv². With lower mass m but same KE, velocity v must be higher. These faster-moving lighter particles collide with walls more frequently due to their higher speed, even though each collision transfers less momentum (since p = mv and m is smaller). The increased collision rate more than compensates for the reduced momentum per collision, resulting in higher pressure overall. Choice A incorrectly assumes lighter particles always create less pressure, ignoring the speed effect. When comparing gases at equal temperature, remember that lighter particles move faster and collide more frequently.
- A sealed rigid container of neon gas is heated. Particles move faster and collide with the walls more often and harder. Which statement best explains the pressure increase?
Answer: The pressure increases because faster particles transfer more momentum per collision and collide more frequently with the walls.
This question tests understanding of kinetic theory of temperature and pressure. When a gas is heated in a rigid container, the average kinetic energy of particles increases, causing them to move faster. These faster-moving particles collide with container walls more frequently and with greater force, transferring more momentum per collision. Since pressure is the force per unit area from these collisions, both increased collision frequency and greater momentum transfer contribute to higher pressure. Choice B incorrectly suggests particle mass changes with temperature, which violates conservation of mass—a common misconception that confuses kinetic energy changes with mass changes. When analyzing pressure changes, remember that pressure depends on collision rate and momentum transfer, both of which increase with particle speed.
- A gas is heated at constant pressure under a movable piston; particles move faster while the piston rises. Which statement best explains why pressure stays constant?
Answer: Pressure stays constant because the rising piston reduces collision frequency per area, offsetting more forceful collisions.
This question tests understanding of kinetic theory of temperature and pressure. In a constant-pressure process, the gas expands as temperature increases, with the piston rising to maintain pressure equilibrium. As particles move faster due to heating, they would normally increase pressure through more forceful collisions, but the rising piston increases the container volume. This volume increase reduces particle density (particles per unit volume), which decreases collision frequency with any given wall area. The two effects—stronger individual collisions but fewer collisions per area—exactly balance to maintain constant pressure. Choice A incorrectly claims heating creates new particles rather than increasing particle speed. For constant-pressure processes, remember that volume must increase proportionally with temperature (Charles's Law).
- A rigid container of gas is cooled. Particles move more slowly, so collisions with the walls are less frequent and transfer less momentum each time. Which statement best explains the pressure change?
Answer: The pressure decreases because reduced particle speeds lower collision rate and momentum transfer.
This question tests understanding of kinetic theory of temperature and pressure. When a gas is cooled, particles lose kinetic energy and move more slowly on average, which has two effects on pressure: particles collide with walls less frequently and each collision transfers less momentum. Both effects work together to reduce the pressure exerted on the container walls. Choice A incorrectly suggests that slower particles increase force by lingering near walls, but pressure depends on momentum transfer rate, not residence time. The fundamental strategy is to recognize that pressure depends on both collision frequency and momentum change per collision, both decreasing when particles slow down.
- Two gases at the same temperature are in identical rigid containers at the same volume and particle number, but one gas has heavier molecules. Which statement best explains the pressures?
Answer: Both gases have the same pressure because equal temperature implies equal average kinetic energy.
This question tests understanding of kinetic theory of temperature and pressure. At the same temperature, particles of different gases have the same average translational kinetic energy (½mv²). Since heavier molecules have greater mass, they must move more slowly to maintain the same kinetic energy as lighter molecules. The pressure depends on momentum transfer rate, which equals mass times velocity times collision frequency. The heavier molecules' greater mass exactly compensates for their lower speed and collision frequency, resulting in equal pressure. Choice A incorrectly assumes mass alone determines pressure without considering velocity. The key insight is that equal temperature means equal average kinetic energy, leading to equal pressure regardless of molecular mass.
