Energy Accounting and Directionality in Thermodynamics (AP Physics 2, Unit 1)

First Law of Thermodynamics

Energy-conservation rule for thermal systems: changes in a system’s internal energy come from heat transfer and work interactions.

First Law (AP Physics sign convention)

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

Internal Energy (U)

Microscopic energy stored in a system (particle kinetic + molecular potential energy); problems usually focus on the change ΔU rather than U itself.

Heat (Q)

Energy transferred because of a temperature difference between a system and its surroundings.

Heat sign convention

Q > 0 means heat flows into the system; Q < 0 means heat flows out of the system.

Work (W) in the First Law

Energy transferred by a force through a distance at the system boundary (often via expansion/compression).

Work sign convention (AP: ΔU = Q − W)

W > 0 when the system does work on the surroundings (system loses energy via work); W < 0 when surroundings do work on the system (system gains energy via work).

State Function

A quantity that depends only on the current state (not the path); for a given start and end state, its change is path-independent.

Path-Dependent Quantity

A quantity whose value depends on the process path between states; heat Q and work W can differ for different paths even if ΔU is the same.

Quasi-static Work (PV work)

For a slow process with well-defined pressure, the work done by a gas equals the area under the curve on a P–V graph: W = ∫P dV.

Constant-Pressure Work

If pressure is constant, work done by the gas is W = PΔV.

Expansion vs. Compression (work sign)

Expansion (ΔV > 0) gives W > 0 (system does work); compression (ΔV < 0) gives W < 0 (work done on system).

Isochoric Process

Constant-volume process (ΔV = 0), so W = 0 and the First Law reduces to ΔU = Q.

Adiabatic Process

No heat transfer (Q = 0), so ΔU = −W; internal energy changes only via work.

Cyclic Process

A process that returns to the initial state; over a full cycle ΔUcycle = 0, so Qnet = W_net.

Second Law of Thermodynamics

Adds directionality to energy transfers: not all energy-conserving processes happen spontaneously; natural processes tend toward greater overall energy dispersal (entropy increase for the universe).

Kelvin–Planck Statement

No cyclic device can take heat from a single reservoir and convert it entirely into work (some waste heat must be rejected).

Clausius Statement

Heat does not spontaneously flow from a colder object to a hotter object.

Heat Engine

A cyclic device that absorbs heat QH from a hot reservoir, rejects heat QC to a cold reservoir, and produces net work output.

Heat Engine Work Output

Over a cycle (ΔU = 0): Wout = QH − Q_C.

Thermal Efficiency (e)

Fraction of input heat converted to work: e = Wout/QH = 1 − (QC/QH); for real engines e < 1.

Refrigerator (energy relation)

A device that uses work input to move heat from cold to hot; over a cycle: QH = QC + W_in.

Coefficient of Performance (COP)

Performance measure for heat movers: refrigerator COP KR = QC/Win; heat pump COP KHP = QH/Win (can be > 1).

Carnot Engine Efficiency

Maximum possible efficiency for any engine operating between TH and TC (in kelvins): eCarnot = 1 − (TC/T_H).

Entropy (S) and Entropy Change

State function measuring energy dispersal/microstate availability; for reversible heat transfer at constant temperature: ΔS = Q_rev/T (T in kelvins).