Every definition and working formula from the six modules, gathered for revision. Fractions are written stacked, exactly as you should on paper. Heat into the system and work done by the gas are taken positive throughout.
0 · Conventions & the first law
◦ Zeroth law: bodies in thermal equilibrium share one temperature — what a thermometer reads.
◦ First law: ΔQ = ΔU + ΔW (heat in = rise in internal energy + work done by the gas).
◦ Heat ΔQ: + when supplied TO the system, − when released.
◦ Work ΔW: + when done BY the gas (expansion), − on compression.
◦ ΔU is a state function (end-states only); ΔQ and ΔW are path functions. Per cycle ΔU = 0.
◦ Ideal gas: U depends on temperature alone, U = (f/2)nRT.
1 · Thermometry & thermal expansion
Temperature — the quantity that decides the direction of heat flow; measured on the Celsius, Fahrenheit or absolute (Kelvin) scale. Absolute zero (0 K) is the point of least molecular motion.
Thermal expansion — most solids grow on heating: linear (α), area/superficial (β) and volume/cubical (γ) coefficients, related α : β : γ = 1 : 2 : 3.
Thermal stress — a rod clamped so it cannot expand develops a compressive stress YαΔT, independent of length.
Anomalous expansion of water — water is densest at 4 °C; between 0 and 4 °C it contracts on heating — why ponds freeze top-down and aquatic life survives.
Specific heat (c) — heat to raise unit mass by one degree; molar specific heat per mole. Heat capacity = mc. Water equivalent w = mc/cwater: the mass of water needing the same heat.
Latent heat (L) — heat per unit mass absorbed or released at a phase change (fusion, vaporisation) at constant temperature — the plateaus on a heating curve.
Principle of calorimetry — in an insulated mix, heat lost by the hot bodies = heat gained by the cold, until a common equilibrium temperature.
Phase (P–T) diagram — maps solid/liquid/gas regions; the triple point is where all three coexist, the critical point ends the liquid–vapour line. Regelation: ice melting under pressure and refreezing.
Ideal gas — point molecules, no forces except at collision; obeys PV = nRT = NkT exactly. Real gases approach it at low pressure, high temperature.
Kinetic pressure — pressure is the drum of molecular impacts on the walls: P = ⅓ρc̄², and the mean translational energy per molecule is ½m c̄² = (3/2)kT — temperature IS molecular kinetic energy.
Molecular speeds — rms > average > most-probable, all ∝ √T. Maxwell distribution: the spread of speeds, peaking at vmp and skewed to high speeds.
Degrees of freedom (f) — independent ways a molecule stores energy (equipartition: ½kT each). Monatomic f = 3, diatomic 5, so Cv = (f/2)R and γ = 1 + 2/f.
Mean free path (λ) — average distance a molecule travels between collisions.
First law — energy conservation: ΔQ = ΔU + ΔW. Work W = ∫P dV is the area under the P–V (indicator) curve; positive on expansion.
Isobaric (const P): W = PΔV. Isochoric (const V): W = 0, ΔQ = ΔU. Isothermal (const T, ideal gas): ΔU = 0, W = nRT ln(V₂/V₁).
Adiabatic — no heat exchange (ΔQ = 0): PVᵞ = const, TVᵞ⁻¹ = const; the gas cools on expansion. Mayer's relation: Cp − Cv = R.
Cyclic process — the gas returns to its start, so ΔU = 0 and the net work equals the enclosed loop area (clockwise = work out).
first law ΔQ = ΔU + ΔWwork W = ∫P dVisobaric W = PΔVisothermal W = nRT lnV₂V₁adiabatic PVᵞ = constadiabatic work W = P₁V₁ − P₂V₂γ − 1Mayer Cp − Cv = R
5 · Heat engines & the second law
Heat engine — takes Qh from a hot source, dumps Qc to a cold sink, and delivers work W = Qh − Qc each cycle. Efficiency η = W/Qh.
Carnot cycle — two isotherms + two adiabats; the most efficient cycle between two temperatures, η = 1 − Tc/Th. No real engine can beat it (Carnot's theorem).
Refrigerator / heat pump — the engine run in reverse: work pumps heat from cold to hot. Rated by coefficient of performance (COP).
Second law — heat will not flow cold → hot unaided (Clausius) and no engine turns all heat into work (Kelvin–Planck). Entropy ΔS = Qrev/T measures the one-way spread of energy.
efficiency η = 1 − QcQhCarnot η = 1 − TcThfridge COP = TcTh − Tcentropy ΔS = QrevT
6 · Heat transfer
Conduction — energy passed molecule to molecule through a solid (Fourier's law). Thermal resistance R = x/KA adds like electrical resistance: series R = R₁ + R₂, parallel 1/R = 1/R₁ + 1/R₂.
Convection — heat carried bodily by a moving fluid (natural, from density differences, or forced).
Radiation — emitted as electromagnetic waves, no medium needed. A blackbody (e = 1) is the perfect emitter/absorber; Kirchhoff: good absorbers are good emitters (e = a). Stefan–Boltzmann: emitted power ∝ T⁴.
Wien's displacement — the emission peak shifts to shorter wavelength as a body heats: hotter looks bluer.
Newton's law of cooling — for a small excess over the surroundings, the rate of cooling is proportional to that excess.
conduction i = KA ΔTx = ΔTRresistance R = xKAStefan u = eσAT⁴net loss eσA(T⁴ − T₀⁴)
Kirchhoff e = aWien λmT = bNewton cooling dTdt = −k(T − T₀)solution T = T₀ + (Ti − T₀)e−kt
Constants: R = 8.314 J mol⁻¹K⁻¹ · k = 1.38×10⁻²³ J K⁻¹ · NA = 6.022×10²³ mol⁻¹ · σ = 5.67×10⁻⁸ W m⁻²K⁻⁴ · Wien b = 2.90×10⁻³ m·K · 0 °C = 273.15 K Compiled from the Vedatom Physics Thermo Lab · every formula has a live, draggable simulation on its module page.