Proven Mnemonics & Acronyms — fast to learn, hard to forget.
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Ideal Gas Law
PV = nRT
Ideal Gas Law
Pressure × Volume = moles × gas constant × Temperature
P = pressure, V = volume, n = moles, R = 8.314 J/mol·K, T = temperature in Kelvin. Compress gas → pressure rises. Heat gas → pressure or volume increases.
Heat Transfer
CCR: Conduction, Convection, Radiation — 3 heat transfer modes
Heat Transfer
Three ways heat moves — remember CCR
Conduction: direct contact (metal spoon in soup). Convection: fluid movement (boiling water). Radiation: electromagnetic waves (sun warming you). Radiation needs no medium.
C
Conduction — contact
C
Convection — fluid movement
R
Radiation — EM waves, no medium needed
Second Law
Entropy always increases in isolated systems — disorder grows
Second Law
Things move from order to disorder spontaneously — never the reverse
A shattered egg never reassembles. Ice melts in warm room but water won't freeze spontaneously. The universe trends toward maximum disorder (maximum entropy).
Carnot Efficiency
Carnot efficiency = 1 - (Tc/Th) — maximum possible efficiency of any heat engine
Carnot Efficiency
No real engine can exceed Carnot efficiency — it's the theoretical maximum
Efficiency depends only on the temperatures of the hot (Th) and cold (Tc) reservoirs in Kelvin. Higher temperature difference → higher efficiency. Real engines always fall short due to irreversibility.
Temperature Scales
Temperature scales: K = °C + 273. Absolute zero = 0 K = -273°C — molecules stop moving.
Temperature Scales
Converting between Celsius and Kelvin — and what absolute zero means
Always use Kelvin in gas law calculations. 0 K (absolute zero): minimum possible temperature, molecules have minimum kinetic energy. Room temperature ≈ 293 K. Water freezes at 273 K, boils at 373 K. Fahrenheit: °F = (9/5)°C + 32.
Specific Heat Capacity
Specific heat capacity: Q = mcΔT. Water has high specific heat — resists temperature change.
Specific Heat Capacity
How much energy is needed to change a substance's temperature
Q = heat energy (J), m = mass (kg), c = specific heat capacity (J/kg·K), ΔT = temperature change. Water: c = 4,186 J/kg·K — very high. Metals: much lower c. High specific heat = more energy needed to heat up = slower temperature change. This is why coastal cities have milder climates.
Thermal Expansion
Thermal expansion: solids, liquids, and gases all expand when heated. Bridges have expansion joints.
Thermal Expansion
Most materials expand when heated and contract when cooled
Linear expansion: ΔL = αLΔT where α = coefficient of linear expansion. Volume expansion: ΔV = βVΔT where β ≈ 3α. Applications: gaps in railroad tracks and bridges (expansion joints), thermostats (bimetallic strips), thermometers. Exception: water expands when it freezes (ice less dense than water).
Heat Engines
Heat engines: take heat from hot reservoir, do work, dump waste heat to cold reservoir
Heat Engines
How all heat engines work — from car engines to power plants
All heat engines follow the same principle: absorb heat Qh from hot source, convert some to work W, reject remaining heat Qc to cold sink. Efficiency = W/Qh = 1 - Qc/Qh. Carnot efficiency is the theoretical maximum: 1 - Tc/Th. Real engines always less efficient due to friction and irreversibility.
Phase Changes
Phase changes: melting, freezing, vaporization, condensation, sublimation. Temperature constant during phase change.
Phase Changes
What happens to temperature during a change of state
During a phase change, temperature stays constant while energy goes into breaking/forming intermolecular bonds. Latent heat of fusion (melting/freezing): energy to change between solid and liquid. Latent heat of vaporization: energy to change between liquid and gas. Q = mL where L = latent heat.
Zeroth Law
Zeroth Law of Thermodynamics: if A=B in temperature and B=C, then A=C. Basis of thermometers.
Zeroth Law
The law that makes temperature measurement possible
If object A is in thermal equilibrium with object B, and object B is in thermal equilibrium with object C, then A and C are in thermal equilibrium with each other. This is why thermometers work — they reach equilibrium with whatever they measure. Called 'zeroth' because it was defined after 1st and 2nd laws.
Q/t = kAΔT/d. k = thermal conductivity (high k = good conductor, low k = good insulator). A = cross-sectional area. ΔT = temperature difference. d = thickness. Metals have high k. Air, wood, foam have low k. R-value (insulation): R = d/k, higher R = better insulator.
Four Laws of Thermodynamics
ZFST — Zeroth (equilibrium), First (energy conservation), Second (entropy), Third (absolute zero)
All four laws of thermodynamics and what each governs
You can remember them as: you must play, you cannot win, you cannot break even, you cannot quit
Zeroth Law: if A is in thermal equilibrium with B and B with C, then A is in equilibrium with C — defines temperature. First Law: ΔU = Q − W — energy is conserved (heat added minus work done by system). Second Law: entropy of isolated system never decreases — heat flows hot to cold, not reverse. Third Law: as T→0 K, entropy→0 (perfect crystal at absolute zero). Mnemonic for 1st and 2nd: you can't win (can't create energy), you can't break even (can't avoid entropy increase).
Zeroth
Thermal equilibrium is transitive — defines temperature measurement
First
ΔU = Q − W — energy conserved, just changes form
Second
Entropy never decreases — irreversibility of natural processes
Entropy and Disorder
S = k ln W — entropy is the number of microstates. More disorder = higher entropy = more probable state.
What entropy actually measures and why it always increases
The universe tends toward higher entropy because there are vastly more disordered states than ordered ones
Boltzmann entropy: S = k_B ln W where W = number of microstates consistent with the macrostate. k_B = 1.38×10⁻²³ J/K. A gas spreading to fill a room: overwhelming number of microstates with gas spread out vs. concentrated — statistically certain to spread. Entropy change: ΔS = Q/T for reversible process. ΔS > 0 for irreversible. Gibbs free energy: G = H − TS. Spontaneous when ΔG < 0. High T favors entropy-driven reactions. Low T favors enthalpy-driven.
S = k ln W
Entropy = Boltzmann constant × ln(number of microstates)
ΔS = Q/T
Entropy change for reversible process — larger at lower T
The four standard thermodynamic processes and what each holds constant
Each process has a simplified version of the first law — learn which term goes to zero for each
Isothermal (constant T): ΔU = 0 for ideal gas → Q = W. PV = constant (Boyle's Law). Isobaric (constant P): W = PΔV. Q = nCpΔT. Adiabatic (no heat exchange, Q = 0): ΔU = −W. TV^(γ-1) = constant. Faster process = more adiabatic. Isochoric/Isovolumetric (constant V): W = 0. ΔU = Q = nCvΔT. PV diagram: isothermal = hyperbola. Adiabatic = steeper hyperbola. Isobaric = horizontal line. Isochoric = vertical line.
Isothermal
T constant → ΔU = 0 → Q = W for ideal gas
Adiabatic
Q = 0 → ΔU = −W → temperature changes as work done
Isochoric
V constant → W = 0 → all heat goes to internal energy
Heat Engines and Refrigerators
Engine: takes heat from hot, does work, dumps heat to cold. Refrigerator: reverse — work in, moves heat from cold to hot.
How heat engines and refrigerators work as thermodynamic cycles
COP of refrigerator = Q_cold / W. COP of heat pump = Q_hot / W. Both limited by Carnot.
Heat engine: Q_H (from hot source) → W (work out) + Q_C (to cold sink). Efficiency η = W/Q_H = 1 − Q_C/Q_H ≤ 1 − T_C/T_H (Carnot limit). Refrigerator: W (work in) moves Q_C from cold reservoir, dumps Q_H = Q_C + W to hot. COP_refrig = Q_C/W = T_C/(T_H−T_C) at Carnot. Heat pump: same as refrigerator but goal is heating. COP_HP = Q_H/W = T_H/(T_H−T_C). Heat pumps can be more than 100% efficient (move more heat than work input) — they move existing heat, not create it.
Engine η
η = W/Q_H ≤ 1 − T_C/T_H — Carnot sets the ceiling
Refrigerator
COP = Q_C/W — how much cold per unit work
Heat pump
COP > 1 possible — moves heat rather than creating it
🎓 Common Exam Questions
Q: State the laws of thermodynamics and give a real-world example of each.
A: Zeroth Law: if system A is in thermal equilibrium with B, and B with C, then A is in equilibrium with C. This defines temperature — a thermometer works because it reaches equilibrium with what it measures. First Law (energy conservation): ΔU = Q − W. A gas heated in a cylinder: heat added → raises internal energy AND does work pushing the piston. Energy is neither created nor destroyed. Second Law (entropy): entropy of an isolated system never decreases. Ice melting in a warm room: heat flows from warm to cold spontaneously. The reverse (cold room spontaneously freezing ice while warming) never happens — it would decrease entropy. Third Law: entropy approaches zero as temperature approaches absolute zero. Perfect crystal at 0 K has exactly one microstate → S = k ln(1) = 0. Practical consequence: impossible to reach absolute zero in finite steps.
Q: Derive the efficiency of a Carnot engine and explain why no real engine can exceed it.
A: Carnot engine: operates between hot reservoir T_H and cold reservoir T_C in four reversible steps: isothermal expansion (absorbs Q_H at T_H), adiabatic expansion, isothermal compression (rejects Q_C at T_C), adiabatic compression. For a reversible process: Q_H/T_H = Q_C/T_C. Efficiency: η = W/Q_H = (Q_H − Q_C)/Q_H = 1 − Q_C/Q_H = 1 − T_C/T_H. Why no real engine exceeds Carnot: Second Law proof — if any engine could exceed Carnot efficiency, you could use it to drive a Carnot refrigerator and create a perpetual motion machine that violates the Second Law. Real engines are always less efficient than Carnot: friction, turbulence, irreversible heat transfer, finite temperature differences. Example: Carnot between 300 K and 600 K → max efficiency = 50%. Real engine achieves perhaps 35–40%.
Q: Explain entropy — what it is, how it is calculated, and why it always increases.
A: Entropy S: a measure of the number of microstates W available to a system: S = k_B ln W (Boltzmann). Macrostate: what we observe (temperature, pressure). Microstate: specific arrangement of all particles. A gas in a box: when gas expands into a vacuum, W increases enormously → S increases → irreversible. Entropy change: ΔS = ∫dQ_rev/T for reversible process. For irreversible: ΔS_universe > 0. For isothermal process: ΔS = Q/T. Why it always increases: the disordered states vastly outnumber ordered states — statistical mechanics explains this without invoking any fundamental 'law of disorder.' A shuffled deck has vastly more arrangements than sorted. Gibbs free energy G = H − TS: at constant T and P, spontaneous processes decrease G. At high T, entropy term dominates. At low T, enthalpy dominates. ΔG = 0: equilibrium.
Q: Compare the three modes of heat transfer with equations and examples.
A: Conduction: heat transfer through direct contact/molecular collisions. Fourier's Law: P = kA(ΔT/Δx) where k = thermal conductivity, A = area, ΔT/Δx = temperature gradient. Good conductors: metals (copper k=400 W/mK). Poor conductors/insulators: wood, foam, air. Used in: cooking pans, heat sinks, building insulation. Convection: heat transfer by bulk fluid motion. Natural: hot fluid rises (less dense), cold sinks — creates circulation. Forced: fan or pump moves fluid. Newton's Law of Cooling: P = hA(T_surface − T_fluid). Used in: radiators, HVAC, ocean currents, weather. Radiation: heat transfer by electromagnetic waves (infrared). Stefan-Boltzmann Law: P = εσAT⁴ where σ = 5.67×10⁻⁸ W/m²K⁴, ε = emissivity (0–1). At absolute zero, radiation = 0 (T⁴ term). Used in: solar energy, thermos bottles, space heating. All three can occur simultaneously — a hot radiator heats by all three modes.
Q: What is the ideal gas law and what assumptions underlie it?
A: Ideal Gas Law: PV = nRT where P = pressure (Pa), V = volume (m³), n = moles, R = 8.314 J/mol·K, T = temperature (K). Or: PV = NkT where N = number of molecules, k = 1.38×10⁻²³ J/K. Assumptions of ideal gas model: (1) Molecules are point particles (negligible volume). (2) No intermolecular forces except during collisions. (3) Collisions are perfectly elastic (no energy lost). (4) Molecules move in random directions with random speeds. Special cases: Boyle's Law (T constant): PV = constant. Charles's Law (P constant): V/T = constant. Gay-Lussac's Law (V constant): P/T = constant. Real gases deviate at: high pressure (molecules have volume), low temperature (intermolecular forces matter). Van der Waals equation: (P + an²/V²)(V − nb) = nRT — corrects for molecular volume (b) and attraction (a). Internal energy of ideal gas: U = (3/2)nRT — depends only on temperature.