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AP Physics 2: Algebra-Based · Unit 1 of 7
Thermodynamics
15–18% of the exam4 lessons · 52 min22 terms
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
- Temperature & Kinetic Theory12 min · 3 objectivesDescribe the postulates of kinetic molecular theory · Relate absolute temperature to the average kinetic energy of molecules · Convert between Celsius and Kelvin and reason on the absolute scale
- The Ideal Gas Law13 min · 3 objectivesState the ideal gas law and identify each variable and its units · Solve for pressure, volume, temperature, or moles given the others · Apply the combined gas law to before-and-after changes in a gas
- Heat, Specific Heat & the First Law14 min · 3 objectivesDistinguish heat, temperature, and internal energy · Use Q = mcΔT to calculate heat transfer and specific heat · Apply the first law of thermodynamics with correct signs for heat and work
- The Second Law, Entropy & Heat Engines13 min · 3 objectivesState the second law of thermodynamics in terms of entropy · Compute the efficiency of a heat engine from heat and work · Calculate the maximum (Carnot) efficiency set by reservoir temperatures
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.
Every term in Unit 1
All 22 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, or PV = NkT with N particles and Boltzmann's constant. Temperature must be in kelvin.
- 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.
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.
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.
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 22 terms with definitions for this unit, all of them on this page.
How should I study Physics 2 Unit 1?
Read the 4 lessons below first — about 50 minutes — then drill the 22 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.