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 T_{K} = T_{C} + 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: $\triangle L = \beta L_{0} \triangle T$, where $\triangle L$ is change in length and $\beta$ depends on the material.

Coefficient of linear expansion (α)

Material-dependent constant in $\triangle L = \beta L_{0} \triangle T$; units of $1/^\text{C}$ (or $1/\text{K}$).

Volume expansion equation

For volume changes: $\triangle V = \beta V_{0} \triangle T$, used especially for liquids (and sometimes solids).

Coefficient of volume expansion (\beta)

Material-dependent constant in $\triangle V = \beta V_{0} \triangle T$; for isotropic solids, \beta \roughly 3\beta 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): $Q = mc \triangle T$.

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 $Q = mc \triangle T$: if an object cools, $\triangle T < 0$ 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 (\epsilon)

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

Stefan–Boltzmann radiation law (net power)

Net radiated power: P = \epsilon \sigma A (T^4 − T_{env}^4), with T in Kelvin and \sigma 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: $\frac{(P_{1}V_{1})}{T_{1}} = \frac{(P_{2}V_{2})}{T_{2}}$ (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 = P ΔV.

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 $\triangle U = -W$, so an ideal gas cools during adiabatic expansion ($W > 0 \rightarrow \triangle U < 0$).

Heat engine

A cyclic device that produces net work by absorbing heat Q_{H} from a hot reservoir and expelling heat Q_{C} to a cold reservoir.

Engine energy relation (W_{net} = Q_{H} − Q_{C})

Over one full engine cycle, ΔU = 0, so net work output equals heat absorbed minus heat expelled: W_{net} = Q_{H} − Q_{C}.

Thermal efficiency (e)

Fraction of input heat converted to net work: e = \frac{W_{net}}{Q_{H}} = 1 − \frac{Q_{C}}{Q_{H}}; for cyclic engines, e < 1.

Carnot efficiency (e_{max})

Maximum possible efficiency for any engine between reservoirs: e_{Carnot} = 1 − \frac{T_{C}}{T_{H}}, with temperatures in Kelvin.

Refrigerator/heat pump coefficient of performance (COP)

Performance measure: COP_{R} = \frac{Q_{C}}{W} (refrigerator removes heat from cold space); COP_{HP} = \frac{Q_{H}}{W} (heat pump delivers heat to warm space).

Second law of thermodynamics

Sets direction/limits: heat flows spontaneously hot $\rightarrow$ 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, $\triangle S = \frac{Q_{rev}}{T}$ (Kelvin). For an isolated system, total entropy does not decrease; irreversible processes increase total entropy.