Unit 9 · Thermodynamics

Kinetic theory of gas pressure ● (core concept) — The model in which a gas's pressure arises from countless collisions of its atoms with each other and with the container walls; each collision transfers momentum to the surface, and the summed perpendicular force components per unit area is the pressure.

Gas pressure (microscopic definition) ● (core concept) — P = F⊥ / A, where F⊥ is the sum of the magnitudes of the perpendicular components of the forces the gas's atoms exert on a surface and A is the surface area. Pressure exists throughout the gas itself, not only at the container walls.

Temperature (kinetic definition) ● (core concept) — A measure of the average kinetic energy of the atoms in a system: higher temperature means the atoms' average kinetic energy is greater.

Maxwell–Boltzmann distribution ● (core concept) — A graph of the distribution of atom energies (or speeds) in a gas at a given temperature. Raising the temperature shifts the peak toward higher energies and broadens the distribution; students are expected to interpret its features, not its functional form.

Root-mean-square speed ● (core concept) — The speed v_rms whose square gives the average of the squared atom speeds in an ideal gas, related to temperature by (1/2)mv_rms² = (3/2)k_BT: hotter gases have faster average molecular motion.

Ideal gas (classical model) ● (core concept) — A gas whose atoms have random instantaneous velocities, negligible atomic volume compared to the container, only elastic collisions, and no appreciable forces except during collisions. PV = nRT = Nk_BT applies to it.

Ideal gas law ● (core concept) — PV = nRT = Nk_BT, relating a gas's pressure P, volume V, amount (n moles or N atoms), and absolute temperature T. R is the universal gas constant and k_B is Boltzmann's constant.

Absolute zero (extrapolation) ● (core concept) — The temperature at which an ideal gas would exert zero pressure, found by extrapolating a graph of pressure versus temperature to P = 0 (0 K, or −273.15 °C).

Thermal contact ● (core concept) — A condition in which two systems may transfer energy by thermal processes (conduction, convection, or radiation). Thermal contact is what makes temperature differences drive energy flow.

Heating ● (core concept) — The transfer of energy INTO a system by thermal processes. Cooling is the transfer of energy OUT of a system by thermal processes.

Conduction ● (core concept) — Energy transfer by thermal processes through direct contact, as faster (hotter) atoms collide with and pass energy to slower (cooler) atoms.

Convection ● (core concept) — Energy transfer by thermal processes in which bulk motion of a fluid (liquid or gas) carries thermal energy from one place to another.

Radiation (thermal) ● (core concept) — Energy transfer by thermal processes via electromagnetic waves, which requires no material medium.

Direction of spontaneous heat transfer ● (core concept) — Energy transferred by thermal processes flows spontaneously from a higher-temperature system to a lower-temperature system — never the reverse without work input. In atomic collisions, energy is most likely transferred from higher-energy atoms to lower-energy atoms.

Thermal equilibrium ● (core concept) — The condition reached when two systems in thermal contact have the same temperature and no net energy is transferred between them by thermal processes.

Internal energy ● (core concept) — The sum of the kinetic energies of the objects making up a system plus the potential energy of their configuration. It can change (e.g., a gas heating up) without the system's center of mass moving.

Internal energy of an ideal monatomic gas ● (core concept) — U = (3/2)nRT = (3/2)Nk_BT: the sum of the kinetic energies of the atoms. Ideal-gas atoms exert no conservative forces on each other and have no internal structure, so there is no internal potential energy.

First law of thermodynamics ● (core concept) — ΔU = Q + W: the change in a closed system's internal energy equals the energy transferred into or out of the system by heating (Q) plus the work done ON the system (W). For an isolated system the total energy is constant. Sign convention: W is work done ON the system.

Pressure-volume work ● (core concept) — W = −PΔV: the work done ON a gas by a constant (or average) external pressure as the gas's volume changes. Compression (ΔV < 0) gives positive work on the gas; expansion gives negative work on the gas.

PV diagram ● (core concept) — A plot of pressure versus volume used to represent thermodynamic processes. Lines of constant temperature are called isotherms, and the magnitude of the work done on a gas during expansion or compression equals the area under the P–V curve.

Isovolumetric process ● (core concept) — A thermodynamic process at constant volume (ΔV = 0), so no pressure-volume work is done and ΔU = Q.

Isothermal process ● (core concept) — A thermodynamic process at constant temperature; for an ideal gas the internal energy does not change (ΔU = 0), so Q = −W.

Isobaric process ● (core concept) — A thermodynamic process at constant pressure; the work done on the gas is W = −PΔV.

Adiabatic process ● (core concept) — A thermodynamic process in which no energy is transferred into or out of the system by thermal processes (Q = 0), so ΔU = W: all internal-energy change comes from work done on the system.

Isolated system ● (core concept) — A system that exchanges no energy or matter with its surroundings. For an isolated system the total energy is constant, and isolated systems spontaneously move toward thermodynamic equilibrium.

Specific heat ● (core concept) — An intrinsic property of a material: the energy per unit mass per degree needed to change its temperature. Related to temperature change by Q = mcΔT. AP Physics 2 models specific heat as independent of temperature.

Thermal conductivity ● (core concept) — An intrinsic property of a material measuring how well it conducts thermal energy. The conduction rate is Q/Δt = kA(ΔT/L), growing with conductivity k, area A, and temperature difference, and shrinking with thickness L.

Second law of thermodynamics ● (core concept) — The total entropy of an isolated system can never decrease, and stays constant only when every process the system undergoes is reversible. Only a qualitative treatment is in scope for AP Physics 2.

Entropy ● (core concept) — A qualitative measure of the tendency of energy to spread out, or of how much of a system's energy is unavailable to do work. Localized energy spontaneously disperses.

Entropy as a state function ● (core concept) — Entropy depends only on a system's current state or configuration, not on the path taken to reach it. Maximum entropy occurs when a system is in thermodynamic equilibrium, which isolated systems drift toward spontaneously.

Entropy: isolated vs. closed systems ● (core concept) — The entropy of an isolated system never decreases. The entropy of a closed (but not isolated) system CAN decrease, because energy can be transferred into or out of it.