AP Physics 2 Thermodynamics: How Processes, PV Diagrams, and Entropy Fit Together

Thermodynamic process

A change that takes a system from one equilibrium state to another; describes the path between states, not just the endpoints.

Equilibrium state

A state describable by state variables (e.g., P, V, T) where macroscopic properties are well-defined and stable.

State variables

Macroscopic quantities (pressure P, volume V, temperature T, etc.) that specify the thermodynamic state.

State function

A quantity that depends only on the initial and final states, not on the path (e.g., U, T, P, V; and changes like ΔU).

Path-dependent quantity

A quantity whose value depends on the specific process/path taken between states (notably heat Q and work W).

Heat (Q)

Energy transfer across the system boundary due to a temperature difference; not “contained” in the gas.

Work (W)

Energy transfer across the system boundary via macroscopic forces/displacement (e.g., PV work); not “contained” in the gas.

First Law of Thermodynamics (AP sign convention)

Energy accounting rule: ΔU = Q − W, where Q is heat added to the system and W is work done by the system.

Internal energy (U)

Microscopic energy of the system (random molecular motion and intermolecular potential energy).

Ideal-gas internal energy property

For an ideal gas, U depends only on temperature, so ΔU depends only on ΔT.

PV work (pressure–volume work)

Work associated with volume change in a piston-cylinder system; incrementally dW = P dV.

Work from a PV diagram

For a process from Vi to Vf, W = ∫ P dV, equal to the area under the P–V curve (often found by geometry in AP Physics 2).

Sign of work in PV processes

Expansion (ΔV > 0) gives W > 0; compression (ΔV < 0) gives W < 0, using W as work done by the gas.

Isobaric process

Constant-pressure process; horizontal line on a PV diagram; work is W = PΔV (often nonzero).

Isochoric process

Constant-volume process; vertical line on a PV diagram; since ΔV = 0, W = 0 and thus ΔU = Q.

Isothermal process (ideal gas)

Constant-temperature process; for an ideal gas ΔU = 0, so Q = W; PV curve slopes downward as V increases.

Adiabatic process

No heat transfer (Q = 0); First Law gives ΔU = −W (adiabatic expansion cools an ideal gas).

Thermodynamic cycle

A set of processes that returns the system to its initial state; over one cycle, ΔUcycle = 0.

Net work in a cycle

Wnet equals the area enclosed by the PV loop; clockwise gives Wnet > 0, counterclockwise gives Wnet < 0.

Macrostate

Description of a system using macroscopic variables (like P, V, T and energy distribution) without molecular detail.

Microstate

A specific detailed molecular arrangement (positions and speeds) consistent with a macrostate.

Multiplicity (Ω)

The number of microstates corresponding to a given macrostate; higher Ω means the macrostate is more probable.

Entropy (statistical definition)

S = k ln Ω; entropy increases with multiplicity (k is Boltzmann’s constant).

Entropy change (thermodynamic definition)

For reversible heat transfer, ΔS = Qrev/T (T in kelvins); adding heat at lower T produces a larger ΔS.

Second Law of Thermodynamics (entropy form)

Total entropy change satisfies ΔStotal = ΔSsystem + ΔSsurroundings ≥ 0; equals 0 for reversible processes and is > 0 for real irreversible processes.