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AP Physics 2: Algebra-Based · Unit 1 of 7

Thermodynamics

Name: AP Physics 2: Algebra-Based Unit 1: Thermodynamics
Availability: InStock

15–18% of the exam7 lessons · 96 min45 terms

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What this unit covers

The topics below follow the published Physics 2 course framework for Unit 1. This unit is worth 15–18% of the exam, so budget your time against that rather than against how long the unit takes to teach.

Kinetic theoryIdeal gas lawHeat enginesLaws of thermodynamics

Lessons in this unit

Formulas in Unit 1

Average translational kinetic energy

KE_avg = (3/2) k_B · T

k_B = 1.38 × 10⁻²³ J·K⁻¹ is Boltzmann’s constant. T must be in kelvin — this relationship only holds on the absolute scale.

Root-mean-square speed

v_rms = √(3 k_B · T / m)

The typical molecular speed grows with √T, not T. Heavier molecules (larger m) move slower at the same temperature.

Ideal gas law

P · V = n · R · T

R = 8.314 J·(mol·K)⁻¹. Use SI units: P in pascals, V in m³, T in kelvin. Then PV has units of joules.

Combined gas law (fixed amount of gas)

P₁V₁ / T₁ = P₂V₂ / T₂

When n is constant, PV/T stays constant. This is the go-to tool for “a gas changes from state 1 to state 2” problems.

Heat and temperature change

Q = m · c · ΔT

c is the specific heat (J·(kg·K)⁻¹): the heat needed to raise 1 kg by 1 K. ΔT = T_final − T_initial, so Q is positive when the object is heated.

First law of thermodynamics

ΔU = Q − W

Q is heat added TO the gas; W is work done BY the gas. Adding heat raises internal energy; letting the gas do work (expand) lowers it.

Thermal efficiency

e = W / Q_H = 1 − (Q_C / Q_H)

Efficiency is the fraction of input heat turned into work. It is always between 0 and 1 (0–100%).

Carnot (maximum) efficiency

e_c = 1 − (T_C / T_H)

The best efficiency any engine can reach between two reservoirs. T_C and T_H must be in kelvin. No real engine beats this ideal limit.

Work on a PV diagram

W_by gas = area under the path · expansion (V increases) → W_by gas positive · compression → W_by gas negative

For a constant-pressure process, W = PΔV. For anything else, read the area.

The four processes

isobaric (P const): W_on = −PΔV · isochoric (V const): W = 0, so ΔU = Q · isothermal (T const): ΔU = 0, so Q = −W · adiabatic (Q = 0): ΔU = W

For an ideal gas ΔU depends only on temperature, which is why constant T means constant U.

Efficiency

e = W / Q_H = 1 − Q_C/Q_H · maximum (Carnot): e_max = 1 − T_C/T_H, with temperatures in KELVIN

Kelvin is not optional. Using Celsius in the Carnot formula produces a nonsense answer, sometimes above 1.

Every term in Unit 1

All 45 terms we publish for Thermodynamics, with definitions. Reading them through is the fastest way to find the ones you cannot define — then drill those in cram mode until you can produce them without the prompt.

Ideal gas law: PV = nRT = Nk_BT. Pressure, volume and absolute temperature of a dilute gas are linked; always use kelvins.
First law of thermodynamics: ΔU = Q + W using the convention that W is work done ON the gas. Energy is conserved; internal energy changes only through heat or work.
Temperature vs thermal energy: Temperature is the average kinetic energy per particle; thermal energy is the total. A bathtub of warm water holds more thermal energy than a boiling cup.
Kinetic theory and temperature: Average translational kinetic energy is (3/2)kT, so absolute temperature is a direct measure of molecular motion.
RMS speed: v_rms = √(3kT/m). At the same temperature, lighter molecules move faster, which is why hydrogen escapes the atmosphere and nitrogen does not.
Maxwell-Boltzmann distribution: The spread of molecular speeds. Raising temperature broadens it and shifts the peak to higher speed.
Internal energy of an ideal gas: Depends only on temperature. An isothermal process has ΔU = 0 no matter how much the volume changes.
PV diagram work: Work is the area under the curve. Clockwise cycles do net work on the surroundings; counterclockwise cycles require net work input.
Isothermal, isobaric, isochoric, adiabatic: Constant temperature (ΔU = 0), constant pressure, constant volume (W = 0), and no heat exchange (Q = 0) respectively.
Second law of thermodynamics: The entropy of an isolated system never decreases. Heat flows spontaneously from hot to cold, never the reverse without work input.
Heat engine efficiency: e = W/Q_H = 1 − Q_C/Q_H. No engine can convert all absorbed heat to work, because some must be rejected to the cold reservoir.
Thermal expansion: Most materials expand on heating as increased vibration raises average atomic separation. Water between 0 and 4 °C is the notable exception.
Conduction, convection, radiation: Conduction transfers energy through direct contact, convection through bulk fluid motion, radiation through electromagnetic waves needing no medium.
Zeroth law: Two systems each in thermal equilibrium with a third are in equilibrium with each other. What makes a thermometer meaningful.
Heat vs temperature vs internal energy: Heat is energy in transit due to a temperature difference; temperature measures average particle kinetic energy; internal energy is the total.
Specific heat capacity: Energy per kilogram per kelvin. Water's is unusually high, which is why coastal climates are mild and why it is used as a coolant.
Latent heat: Energy absorbed during a phase change at constant temperature, spent breaking intermolecular bonds rather than raising kinetic energy.
Why a PV cycle's enclosed area is net work: Work is the area under each leg; going round a loop, the areas partly cancel and the enclosed region is what remains.
Entropy and probability: Entropy measures the number of microscopic arrangements. Systems evolve toward macrostates with more arrangements, which is why disorder increases.
Ideal gas process on a PV diagram: Isobaric is horizontal, isochoric vertical, isothermal a hyperbola, and adiabatic steeper than the isotherm through the same point.
Degrees of freedom qualitatively: A monatomic gas stores energy only in translation, a diatomic also in rotation, which is why their specific heats differ.
Thermal equilibrium in mixing problems: Heat lost by the hotter body equals heat gained by the cooler one, assuming an insulated container.
Work on a PV diagram: The area under the process path. Expansion gives positive work BY the gas, compression negative. Constant volume gives zero work however much P and T change.
Why work is path-dependent: Two paths joining the same states enclose different areas. Internal energy is a state function; work and heat are not.
Net work of a cycle: The enclosed area. Clockwise is positive net work by the gas — a heat engine. Counterclockwise is a refrigerator or heat pump.
Isobaric: Constant pressure, so W = PΔV is easy to compute directly.
Isochoric: Constant volume, so W = 0 and the first law reduces to ΔU = Q. Every joule of heat raises the temperature.
Isothermal: Constant temperature, so ΔU = 0 for an ideal gas and Q = −W. Heat flows in exactly as fast as work is done.
Adiabatic: No heat exchange, so Q = 0 and ΔU = W. Adiabatic compression HEATS the gas; adiabatic expansion COOLS it.
Why adiabatic is steeper than isothermal: The expanding gas cools because it draws the work from its own internal energy, so pressure falls faster than at constant temperature.
Heat engine energy balance: W = Q_H − Q_C. The rejected heat is not a design flaw — the second law makes it unavoidable.
Efficiency and the Carnot ceiling: e = W/Q_H = 1 − Q_C/Q_H. Maximum is 1 − T_C/T_H with temperatures in KELVIN. Celsius gives nonsense, sometimes above 1.
Why 100% efficiency is impossible: It would require T_C = 0 K. Efficiency rises with a hotter source or a colder sink, and reaches 1 only in an unattainable limit.
Coefficient of performance: Heat moved per unit of work for a refrigerator. It can exceed 1 without violating anything — you are relocating heat, not creating energy.
What internal energy depends on: For an ideal gas, temperature alone. This is why isothermal means ΔU = 0 regardless of how much the volume changed.
Ideal gas law forms: PV = nRT with n in moles and R = 8.31 J/(mol·K), or PV = NkT with N molecules and k = 1.38 × 10⁻²³ J/K.
Kelvin is not optional: Every gas-law and Carnot calculation needs absolute temperature. Celsius works only for a temperature DIFFERENCE.
Why a cycle has ΔU = 0: Internal energy is a state function, so returning to the same state returns the same U. The first law then gives Q = W over the cycle.
Reading engine versus refrigerator off a PV loop: Clockwise means positive net work by the gas — an engine. Counterclockwise means work is done on the gas to move heat uphill — a refrigerator or heat pump.
Root-mean-square speed: v_rms = √(3kT/m). Depends on temperature and molecular mass only, so at the same temperature lighter molecules move faster.
Average kinetic energy per molecule: (3/2)kT. Depends on temperature ALONE — the same for every gas at the same temperature, whatever the molecular mass.
Temperature is not heat: Temperature measures average molecular kinetic energy; heat is energy in transit because of a temperature difference. A large cool object can hold more thermal energy than a small hot one.
Specific heat and phase change: Q = mcΔT while the temperature changes, and Q = mL during a phase change where the temperature does NOT change. A heating-curve question needs both.
Three modes of heat transfer: Conduction through direct contact, convection by bulk fluid motion, radiation by electromagnetic waves needing no medium.
Second law, stated usefully: Heat does not flow spontaneously from cold to hot, and no cyclic engine converts heat entirely to work. Entropy of an isolated system does not decrease.

What examiners penalize here

Two proportionalities to lock in: KE_avg ∝ T (linear in absolute temperature), but v_rms ∝ √T. When a problem doubles the temperature, energy doubles while speed rises only by √2.
When a problem gives “before” and “after” states, reach for P₁V₁/T₁ = P₂V₂/T₂ and cancel whatever is held constant. Constant V → P ∝ T; constant T → P ∝ 1/V; constant P → V ∝ T.
Read the wording carefully: “work done ON the gas” is the opposite sign of the W in ΔU = Q − W (which is work done BY the gas). Compression → gas does negative work → U tends to rise; expansion → gas does positive work → U tends to fall.
Compare the two efficiencies: e = 1 − Q_C/Q_H uses the actual heat flows, while e_c = 1 − T_C/T_H is the temperature-set ceiling. A real engine’s efficiency is always less than its Carnot limit — if a problem’s engine beats Carnot, you have an error.
Label the axes P and V and mark the direction of travel with an arrow. Rubrics award the direction, and it is what determines whether the cycle is an engine or a refrigerator.
Write down which term is zero before doing any arithmetic — "adiabatic, so Q = 0" or "isochoric, so W = 0". That single line makes the first law solvable and is often awarded on its own.
If a question gives you both the actual and the Carnot efficiency, it usually wants you to comment on the gap. Say that the shortfall reflects irreversibilities — friction, finite-rate heat transfer, turbulence — rather than a violation of anything.

Practice Physics 2

Our practice bank is drawn from across the whole course rather than filtered to one unit, which is closer to how the exam asks anyway — it will not tell you which unit a question is testing.

194 practice questionsEvery one with a written explanation FRQ trainerWritten answers scored against the rubric Physics 2 study guideAll units, weights and score data in one place All 7 Physics 2 unitsThe full course

Questions about this unit

How much of the AP Physics 2: Algebra-Based exam is Unit 1?

Unit 1, Thermodynamics, is worth 15–18% of the Physics 2 multiple-choice section according to the published course framework. Across all 7 units that makes it a substantial share — heavier than an even split would give it.

What topics are covered in Physics 2 Unit 1?

Thermodynamics covers Kinetic theory, Ideal gas law, Heat engines and Laws of thermodynamics. We publish 45 terms with definitions for this unit, all of them on this page.

How should I study Physics 2 Unit 1?

Read the 7 lessons below first — about 95 minutes — then drill the 45 terms in cram mode until you can produce each definition from memory rather than just recognize it. Recognition is what makes a unit feel finished when it is not. Finish with practice questions and read the explanation for every one you get right by elimination as well as the ones you miss.

All 7 units of AP Physics 2: Algebra-Based

Unit names, topics and exam weights follow the published College Board course framework for AP Physics 2: Algebra-Based. AP® is a trademark registered by the College Board, which does not endorse this site.