AP Physics 2 Thermodynamics: Building Thermal Concepts and Heat Transfer from First Principles

Thermodynamic system

The part of the universe chosen for analysis in a thermodynamics problem (e.g., a gas in a cylinder or coffee in a cup).

Surroundings

Everything outside the system boundary that can interact with the system (exchange energy and/or matter).

System boundary

The (often imaginary) surface that separates the system from the surroundings; what crosses it determines heat/work/mass transfer accounting.

Open system

A system that can exchange both matter and energy with the surroundings (e.g., boiling water in an open pot).

Closed system

A system that can exchange energy but not matter with the surroundings (e.g., sealed gas in a cylinder with a movable piston).

Isolated system

A system that exchanges neither matter nor energy with the surroundings (idealized: perfectly sealed and perfectly insulated).

State variable (state function)

A macroscopic quantity that depends only on the system’s current state, not the path taken (e.g., P, V, T, internal energy).

Thermal equilibrium

A condition where temperature is stable (and typically uniform) so there is no net heat transfer driven by temperature differences.

Zeroth Law of Thermodynamics

If A is in thermal equilibrium with C and B is in thermal equilibrium with C, then A and B are in thermal equilibrium (basis for the meaning of temperature and thermometers).

Heat

Energy transfer across the system boundary due to a temperature difference; not energy “stored” in an object.

Internal energy

Energy contained within a system at the microscopic level (random molecular motion/interactions); changes via heat and/or work transfers.

Work (thermodynamic)

Energy transfer across the boundary due to a force acting through a distance (commonly a gas pushing on a piston).

PV work (constant external pressure)

For expansion/compression against constant external pressure, the work done by the gas is W = PΔV; expansion (ΔV>0) gives positive W, compression gives negative W.

Pressure

Force per unit area: P = F/A; in gases it arises from molecular collisions with container walls. Unit: pascal (Pa = N/m²).

Ideal gas model

A model where gas molecules are point particles with negligible volume, no intermolecular forces (except during elastic collisions), and random motion; valid when gases are dilute and not near condensation.

Ideal Gas Law

Relationship among state variables for an ideal gas: PV = nRT (P pressure, V volume, n moles, T in kelvins, R ideal gas constant).

Combined gas law (fixed n)

For a constant amount of gas between two equilibrium states: (P₁V₁)/T₁ = (P₂V₂)/T₂ (T must be in kelvins).

Kelvin temperature conversion

Convert Celsius to kelvins for gas laws (and radiation): TK = TC + 273.15 (often +273 for AP approximations).

Kinetic theory

Microscopic model connecting particle motion/collisions to macroscopic gas properties like pressure and temperature.

Average translational kinetic energy (ideal gas)

For an ideal gas molecule: Kavg = (3/2)kBT, showing temperature is proportional to average kinetic energy per particle.

Root-mean-square speed

A typical molecular speed: vrms = √(3kBT/m); at the same T, lighter molecules have higher vrms, and vrms ∝ √T.

Specific heat

Energy required to raise the temperature of 1 kg of a material by 1 K; used in Q = mcΔT for temperature changes without phase change.

Latent heat

Energy per kg required for a phase change at constant temperature; phase-change energy is Q = mL (e.g., melting/boiling).

Calorimetry

Energy-conservation approach to thermal interactions; in an insulated (isolated) setup, the net heat exchange sums to zero: ΣQ = 0 (heat lost = heat gained).

Conduction

Heat transfer through direct molecular collisions in a material; steady-state slab model: Q/t = kA(Th−Tc)/L (larger A or ΔT increases rate; larger L decreases rate).