AP Physics 2 Unit 1 Study Notes: Thermodynamics (Algebra-Based)

Temperature

A measure related to the average random kinetic energy of the microscopic particles in a substance (higher average particle speed → higher temperature).

Thermal equilibrium

The condition in which two systems in contact have the same temperature and therefore stop exchanging energy due to a temperature difference.

Zeroth law of thermodynamics

If system A is in thermal equilibrium with system C, and system B is in thermal equilibrium with system C, then A and B are in thermal equilibrium with each other (basis for temperature measurement).

Heat (Q)

Energy transferred across a system boundary due to a temperature difference (not something an object “contains”).

Internal energy (U)

The total microscopic energy of a system (random kinetic energy + intermolecular potential energy).

Thermometer

A device that measures temperature by reaching thermal equilibrium with an object and using a property that changes predictably with temperature.

Kelvin scale

The absolute temperature scale used in thermodynamics; many formulas require temperatures in Kelvin.

Celsius-to-Kelvin conversion

Convert Celsius to Kelvin using TK = TC + 273.15 (often approximated as +273).

Thermal expansion

The tendency of most materials to increase in size when temperature increases (particles vibrate with larger amplitude and take up more space).

Linear expansion equation

For a solid rod: ΔL = αL₀ΔT, where ΔL is change in length and α depends on the material.

Coefficient of linear expansion (α)

Material-dependent constant in ΔL = αL₀ΔT; units of 1/°C (or 1/K).

Volume expansion equation

For volume changes: ΔV = βV₀ΔT, used especially for liquids (and sometimes solids).

Coefficient of volume expansion (β)

Material-dependent constant in ΔV = βV₀ΔT; for isotropic solids, β ≈ 3α when appropriate.

Specific heat capacity (c)

Energy required to raise the temperature of 1 kg of a substance by 1°C (or 1 K).

Sensible heat equation (Q = mcΔT)

Model for heat that changes temperature (no phase change): Q = mcΔT.

Calorimetry (ΣQ = 0)

Energy-conservation method for thermal interactions in an isolated system: the sum of all heat transfers equals zero.

Calorimetry sign convention

In Q = mcΔT: if an object cools, ΔT < 0 so Q < 0 (releases energy); if it warms, Q > 0 (absorbs energy).

Latent heat (Q = mL)

Energy transferred during a phase change at constant temperature: Q = mL (temperature can stay constant while energy changes intermolecular potential energy).

Latent heat of fusion (L_f)

Latent heat constant for melting/freezing processes in Q = mL_f.

Latent heat of vaporization (L_v)

Latent heat constant for boiling/condensing processes in Q = mL_v.

Heating curve

A graph of temperature vs energy added showing sloped regions (use Q = mcΔT) and flat plateaus during phase changes (use Q = mL).

Conduction

Heat transfer through direct contact via microscopic collisions; in metals, mobile electrons contribute strongly.

Conduction power equation

Steady-state heat transfer rate through a slab: P = (kAΔT)/L, where k is thermal conductivity.

Convection

Heat transfer by bulk motion of a fluid (liquid/gas), often driven by density differences (warm rises, cool sinks).

Thermal radiation

Heat transfer by electromagnetic waves; does not require matter, so it works through a vacuum (e.g., Sun warming Earth).

Emissivity (ε)

A surface property (0 to 1) describing how effectively an object emits/absorbs thermal radiation; shiny surfaces have low ε.

Stefan–Boltzmann radiation law (net power)

Net radiated power: P = εσA(T^4 − T_env^4), with T in Kelvin and σ the Stefan–Boltzmann constant.

Ideal gas

A gas model where particles have negligible volume, no intermolecular forces except during collisions, and perfectly elastic collisions (best at low pressure and high temperature).

Ideal gas law (PV = nRT)

Relates macroscopic gas variables: PV = nRT, where T is in Kelvin and P is absolute pressure.

Combined gas law

For fixed amount of gas: (P₁V₁)/T₁ = (P₂V₂)/T₂ (temperatures must be in Kelvin).

Kinetic molecular theory

Microscopic model linking gas behavior to particle motion and collisions; supports gas laws conceptually.

Average translational kinetic energy ∝ T

For an ideal gas, the average translational kinetic energy of particles is proportional to absolute temperature (Kelvin).

PV diagram

A graph of pressure (vertical axis) vs volume (horizontal axis) used to visualize thermodynamic processes and work.

Work done by a gas (dW = PdV)

For a small volume change, incremental work by the gas is dW = P dV (expansion → positive work by the gas).

Constant-pressure work (W = PΔV)

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

Work as area under PV curve

On a PV diagram, the work done by the gas between Vi and Vf equals the area under the process curve.

Thermodynamic cycle

A sequence of processes that returns a system to its initial state (ΔU_cycle = 0).

Net work in a PV cycle

Net work over a closed PV loop equals the area enclosed; clockwise loop → positive net work by the gas, counterclockwise → negative.

First law of thermodynamics (ΔU = Q − W)

Energy accounting for a system: change in internal energy equals heat added to the system minus work done by the system.

Isochoric process

Constant-volume process: ΔV = 0 so W = 0, therefore ΔU = Q (heating raises T and P).

Isobaric process

Constant-pressure process: W = PΔV; heat input typically increases internal energy and does expansion work.

Isothermal process

Constant-temperature process; for an ideal gas, ΔU = 0, so heat added equals work done: Q = W.

Adiabatic process

No heat transfer (Q = 0); thus ΔU = −W, so an ideal gas cools during adiabatic expansion (W > 0 → ΔU < 0).

Heat engine

A cyclic device that produces net work by absorbing heat QH from a hot reservoir and expelling heat QC to a cold reservoir.

Engine energy relation (Wnet = QH − Q_C)

Over one full engine cycle, ΔU = 0, so net work output equals heat absorbed minus heat expelled: Wnet = QH − Q_C.

Thermal efficiency (e)

Fraction of input heat converted to net work: e = Wnet/QH = 1 − (QC/QH); for cyclic engines, e < 1.

Carnot efficiency (e_max)

Maximum possible efficiency for any engine between reservoirs: eCarnot = 1 − (TC/T_H), with temperatures in Kelvin.

Refrigerator/heat pump coefficient of performance (COP)

Performance measure: COPR = QC/W (refrigerator removes heat from cold space); COPHP = QH/W (heat pump delivers heat to warm space).

Second law of thermodynamics

Sets direction/limits: heat flows spontaneously hot → cold, and no cyclic engine can convert all absorbed heat into work (must reject some heat).

Entropy (S)

State function tracking energy dispersal; for reversible heat transfer at constant T, ΔS = Q_rev/T (Kelvin). For an isolated system, total entropy does not decrease; irreversible processes increase total entropy.