Kinetic theory says a gas is a huge number of tiny particles moving randomly and colliding elastically with each other and the container. Each collision with a wall changes a molecule’s momentum; by conservation of momentum that change corresponds to a force on the wall. Pressure is the net perpendicular force per unit area from many such collisions: P = F⊥/A. Microscopically, pressure comes from the sum of momentum transfers per second from molecular bombardment throughout the gas (not just at the boundary). Temperature measures the average translational kinetic energy of those atoms: Kavg = (3/2)kB T = ½ m vrms², so higher T → faster molecules → larger momentum changes per collision → higher P. For AP exam scope you should be comfortable analyzing 1D/2D elastic collisions and relating atomic motion to pressure and temperature; you don’t need the full Maxwell–Boltzmann function (CED 9.1.A/B). Review this topic on Fiveable (study guide: https://library.fiveable.me/ap-physics-2-revised/unit-1/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3), and practice problems at (https://library.fiveable.me/practice/ap-physics-2-revised).

Pressure comes from lots of tiny, rapid collisions of gas atoms with surfaces. Each atom that strikes a wall changes its momentum (usually reversing the perpendicular component of its velocity), so by conservation of momentum the wall must get an impulse. Force is impulse per time; add the perpendicular forces from all collisions and divide by the wall area to get pressure: P = F⊥/A (CED 9.1.A.1.ii). Because atoms move in all directions, collisions happen everywhere in the gas—pressure exists throughout the gas, not only at the boundary (CED 9.1.A.1). The rate and strength of these collisions depend on atomic speeds, which tie to temperature via average kinetic energy Kavg = (3/2)kB T and vrms (CED 9.1.B.1): hotter gas → faster atoms → bigger momentum changes per hit and more frequent hits → higher pressure. For a quick review of these ideas, see the Topic 9.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-1/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3). Practice problems are at (https://library.fiveable.me/practice/ap-physics-2-revised).

Temperature is basically a measure of how much kinetic energy the atoms have on average. In the kinetic theory for an ideal monatomic gas the AP CED gives the key relation: Kavg = (3/2) kB T = (1/2) m v_rms^2. So if the atoms move faster (larger v_rms) their average kinetic energy goes up, and that shows up as a higher temperature. Physically, faster atoms hit each other and the container walls harder and more often, changing momentum and producing pressure (use conservation of momentum for collisions per 9.1.A). The Maxwell–Boltzmann distribution just shows that raising T shifts the whole speed distribution to higher speeds (you don’t need its functional form on the exam, just the idea). For more AP-aligned review see the Topic 9.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-1/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3) and unit resources (https://library.fiveable.me/ap-physics-2-revised/unit-9). Practice problems: (https://library.fiveable.me/practice/ap-physics-2-revised).

Pressure at the walls and pressure inside the gas are the same quantity in equilibrium—pressure exists everywhere in the gas, not just at the boundary (CED 9.1.A.1.iii). Microscopically, pressure comes from atoms colliding and exchanging momentum. At the walls those collisions transfer perpendicular momentum to the surface, producing a force/area P = F⊥/A (CED 9.1.A.1.ii). Inside the gas, atoms collide with each other; those collisions transmit momentum through the fluid so a local small-volume patch feels the same average force/area as the wall would. Key caveat: if the gas isn’t in equilibrium (flows, temperature or density gradients), pressure can vary from place to place. For AP problems you only need to analyze collisions qualitatively or in 1–2D using conservation of momentum and the idea that temperature ↔ average kinetic energy (CED 9.1.B.1). For more review, see the Topic 9.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-1/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3) and more practice at the unit page (https://library.fiveable.me/ap-physics-2-revised/unit-9) or the practice bank (https://library.fiveable.me/practice/ap-physics-2-revised).

Think of gas collisions as lots of tiny, almost-instantaneous elastic hits. In an ideal gas model each atom moves straight until it collides with another atom or the container wall. For a collision between two atoms (or an atom and a fixed wall) you use conservation of momentum; for elastic collisions kinetic energy is conserved too. When an atom bounces off a wall its perpendicular momentum changes Δp⊥, and repeated impacts over time produce a perpendicular force F⊥ = (total Δp⊥/Δt). Pressure is that force per area: P = F⊥/A. Microscopically pressure comes from molecular bombardment everywhere in the gas, not just at the wall. Temperature measures the average translational kinetic energy of atoms (Kavg = 3/2 kB T), so hotter gas → faster atoms → bigger Δp and higher pressure (for fixed volume). AP expectations: analyze collisions qualitatively or quantitatively in 1D/2D using momentum (and KE for elastic cases), and know v_rms relations. For a focused review, check the Topic 9.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-1/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

The Maxwell–Boltzmann distribution is the curve that shows how many gas atoms have each speed (or kinetic energy) at a given temperature. It tells you the most probable speed, how wide the spread of speeds is, and how the tail extends to high speeds. We care about it because temperature is really a measure of average kinetic energy—features of that distribution (peak position, width, and high-speed tail) change with T and determine things like rms speed and pressure from atomic collisions (CED 9.1.B.1 and 9.1.A.1). You don’t need the exact formula for the AP exam—just know qualitatively that increasing T shifts the peak to higher speeds and broadens the curve, and that K_avg = (3/2)kB T = (1/2) m v_rms^2. For a quick review, check the Topic 9.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-1/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Use the AP formula that links temperature to average translational kinetic energy: K_avg = (3/2) k_B T = (1/2) m v_rms^2 How to use it: - If you know K_avg and need T: T = 2 K_avg / (3 k_B). Example: if K_avg = 4.14×10^-21 J, T = 2(4.14×10^-21)/(3·1.38×10^-23) ≈ 200 K. - If you know v_rms (molecular speed) and need T: T = m v_rms^2 / (3 k_B). Use m in kg (mass of one molecule). - If you know T and want v_rms: v_rms = sqrt(3 k_B T / m). Constants and notes: - Boltzmann constant k_B = 1.38×10^-23 J/K. - AP Topic 9.1 treats temperature as a measure of average kinetic energy of atoms (translational degrees of freedom). Use this relation on problems involving ideal monatomic gases or where translational kinetic energy is implied (CED 9.1.B.1). For more examples and practice, check the Topic 9.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-1/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3) and the AP Physics 2 practice set (https://library.fiveable.me/practice/ap-physics-2-revised).

Think of v_rms as the “typical” speed of gas atoms that links temperature to kinetic energy. Technically it’s the square root of the average of the squares of the speeds, so v_rms = sqrt(⟨v²⟩). That definition matters because squaring gives more weight to faster particles, then you take the square root to get back to speed units. For an ideal monatomic gas it directly connects to temperature through 1/2 m v_rms² = 3/2 k_B T, so higher T → larger v_rms → atoms move faster on average. Note: v_rms is not exactly the same as the average speed (⟨v⟩) or the most probable speed from the Maxwell–Boltzmann curve, but AP Physics 2 only expects you to know how v_rms relates to average kinetic energy and temperature, not the full MB functional form. For a quick review see the Topic 9.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-1/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Pressure isn't just at the walls because it's produced by molecules everywhere inside the gas. Every atom is constantly moving and colliding with other atoms; each collision transfers momentum. Those collisions exert tiny forces on neighboring atoms, so if you imagine any small internal surface (real or imaginary) the perpendicular components of those forces per area give a pressure (P = F⊥/A). In an equilibrium gas these molecular impacts are random and roughly isotropic, so the pressure is the same at every point. The CED states this explicitly (9.1.A.1.iii): pressure exists throughout the gas, not only at the container boundary. For AP work, you should be able to explain this in terms of atomic motion and momentum transfer and analyze simple collisions in 1–2 dimensions. For a quick review, see the Topic 9.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-1/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3) and try practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Conservation of momentum just means momentum is conserved in each collision between atoms (or an atom and a surface). For elastic atom–atom collisions, the vector sum of the two atoms’ momenta before = after, so you can analyze 1D or 2D collisions (AP only expects those). For collisions with a fixed container wall, treat the wall as effectively infinite mass: the atom’s perpendicular momentum reverses, Δp⊥ ≈ −2m v⊥ (elastic), and that momentum change delivered per collision divided by collision time gives the average force on the wall. Summing the perpendicular momentum transfer from many atoms and dividing by area gives pressure: P = F⊥/A (CED 9.1.A.1.ii). This connects microscopic momentum conservation to macroscopic pressure; temperature ties in because higher T → larger average |v| and more frequent/larger momentum transfers (CED 9.1.B.1). For a quick review, see the Topic 9.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-1/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3). For extra practice, check Unit 9 and the AP practice problems (https://library.fiveable.me/ap-physics-2-revised/unit-9) and (https://library.fiveable.me/practice/ap-physics-2-revised).

When temperature increases, the Maxwell–Boltzmann speed distribution shifts and spreads: the peak moves to higher speeds (most probable speed increases), the curve becomes broader and its maximum height decreases, and the tail at high speeds gets heavier. Physically that happens because average kinetic energy rises (Kavg = 3/2 kBT), so v_rms and characteristic speeds scale like √T. The total area under the curve stays the same (same number of particles), but a larger fraction of molecules occupy higher-speed bins, which explains higher pressure and faster collisions on container walls. For AP Physics 2 you only need this qualitative picture and the relation between temperature and average kinetic energy / v_rms—you don’t need the explicit functional form (CED 9.1.B.1 and 9.1.B.1.i). For a quick review, check the Topic 9.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-1/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Think of pressure as the push from lots of tiny collisions per second on a surface. One gas atom hits the wall, its perpendicular (normal) momentum changes Δp when it bounces (use conservation of momentum for elastic collisions). The wall feels a force from that change in momentum: F ≈ Δp / Δt. Now sum that force from all atoms hitting a patch of wall in a given time—that gives the total normal force on that patch. Divide by the patch area A and you get pressure: P = F⊥/A (CED 9.1.A.1.ii). So pressure = average momentum transfer per collision × collision rate per area. Because collision rate and momentum transfer depend on atom speeds, pressure links to temperature through the atoms’ average kinetic energy (CED 9.1.B.1). This idea applies everywhere in the gas, not just at the boundary (CED note). For more review, see the Topic 9.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-1/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3) or the unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-9). Practice problems are at (https://library.fiveable.me/practice/ap-physics-2-revised).

Temperature is just a measure of how fast atoms are moving on average. In the kinetic theory for an ideal gas the average translational kinetic energy per atom is Kavg = (3/2) kB T, which you can also write as (1/2) m v_rms^2—so higher T means larger average speeds (v_rms) and more kinetic energy. The Maxwell–Boltzmann distribution shows that as T rises the whole speed-distribution widens and its peak shifts to higher speeds (you don’t need the exact functional form for the AP exam, just the qualitative idea). Pressure comes from many atoms hitting the container walls (momentum change per collision summed over area). For AP review, this is Topic 9.1 (see the study guide (https://library.fiveable.me/ap-physics-2-revised/unit-1/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3)); practice problems are at (https://library.fiveable.me/practice/ap-physics-2-revised).

Temperature is a measure of the average translational kinetic energy of the atoms or molecules in a gas. For an ideal monatomic gas the CED relation is Kavg = (3/2) kB T = (1/2) m vrms^2, so the root-mean-square speed vrms = sqrt(3 kB T / m). That means if the gas temperature doubles, vrms increases by sqrt(2)—molecules move faster, on average, but not twice as fast. The Maxwell–Boltzmann distribution shifts to higher speeds (and broadens) as T increases. Faster-moving molecules hit the container walls more often and with greater momentum change, producing higher pressure (pressure = force⊥/area), consistent with 9.1.A and 9.1.B in the CED. For a quick review, see the Topic 9.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-1/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3). For more practice, try problems in the Unit 9 review (https://library.fiveable.me/ap-physics-2-revised/unit-9) and the practice set (https://library.fiveable.me/practice/ap-physics-2-revised).

Atoms in a gas exert forces because they interact when they collide: each atom is made of charged particles, so short-range electromagnetic forces act during close approaches and when an atom hits the container wall. Those collisions change an atom’s momentum (use conservation of momentum for analysis), so the atom exerts a force on whatever it hits and that object exerts an equal-and-opposite force back. Pressure is just the net result of many such perpendicular force components per unit area (P = F⊥/A), and because collisions happen everywhere, pressure exists throughout the gas, not only at the walls. Temperature ties in because higher T → higher average kinetic energy → faster atoms → more frequent and stronger momentum changes on collision, so pressure increases. For AP-style questions focus on collisions (1D or 2D), momentum conservation, and the link between Kavg = (3/2)kBT and vrms. See the Topic 9.1 study guide for review (https://library.fiveable.me/ap-physics-2-revised/unit-1/1-kinetic-theory-of-temperature-and-pressure/study-guide/wWjb2NGJDLNmMhB3) and unit resources (https://library.fiveable.me/ap-physics-2-revised/unit-9). For practice, check the AP practice set (https://library.fiveable.me/practice/ap-physics-2-revised).