01 · Foundations
The four laws of thermodynamics
0th Law
Thermal equilibrium
If A is in thermal equilibrium with B, and B with C, then A is in equilibrium with C. This defines temperature as a measurable property.
1st Law
Conservation of energy
Energy cannot be created or destroyed, only converted between forms. ΔU = q + w (internal energy = heat + work).
2nd Law
Entropy increases
The total entropy of an isolated system always increases in a spontaneous process. The universe tends toward maximum disorder.
3rd Law
Absolute zero
The entropy of a perfect crystal at absolute zero (0 K) is zero. Absolute zero cannot be reached in finite steps.
The First Law (ΔU = q + w) is the starting point for all energy calculations. In chemistry, the most common work term is pressure-volume work: w = −pΔV. At constant pressure (typical of laboratory reactions open to atmosphere), heat flow equals the enthalpy change: qp = ΔH.
02 · Enthalpy
Enthalpy: heat at constant pressure
Enthalpy (H) is defined as H = U + pV. For a process at constant pressure, ΔH = ΔU + pΔV. The practical significance: ΔH is the heat that flows into or out of a reaction flask open to the atmosphere.
ΔH = H(products) − H(reactants)
Exothermic: ΔH < 0
Endothermic: ΔH > 0
Standard enthalpy values (ΔH°) are measured at 298 K and 100 kPa. Standard enthalpies of formation (ΔHf°) are tabulated for most compounds and allow calculation of reaction enthalpies via:
ΔH°rxn = Σ ΔHf°(products) − Σ ΔHf°(reactants)
Bond enthalpies provide an alternative route: breaking bonds requires energy (endothermic); forming bonds releases energy (exothermic). The net ΔH ≈ Σ bonds broken − Σ bonds formed. This connects to chemical bonding and explains why combustion (breaking weak C–H and O=O bonds, forming strong C=O and O–H bonds) is always exothermic.
03 · Entropy
Entropy and the Second Law
Entropy (S) measures disorder — more precisely, the number of microscopic arrangements (microstates) consistent with the observed macrostate. Boltzmann's relation: S = kB ln Ω.
Predicting the sign of ΔS:
- ΔS > 0 — solid dissolves, gas is produced, number of gas moles increases, mixing occurs.
- ΔS < 0 — gas condenses, precipitate forms, number of gas moles decreases.
The Second Law states that the entropy of the universe (system + surroundings) always increases in a spontaneous process: ΔSuniv > 0. This is why heat flows from hot to cold (never spontaneously the reverse), why gases expand to fill containers, and why concentrated solutions dilute.
In biology, living organisms maintain highly ordered states locally — but they do so by increasing the entropy of their surroundings (releasing heat from respiration). The net ΔSuniv remains positive. See Cellular respiration for how cells couple exothermic ATP hydrolysis to endothermic biosynthesis.
04 · Gibbs free energy
Gibbs free energy: the spontaneity criterion
The Gibbs free energy (G) combines enthalpy and entropy into a single spontaneity criterion for processes at constant temperature and pressure:
ΔG = ΔH − TΔS
At equilibrium, ΔG = 0, and the relationship to the equilibrium constant K:
ΔG° = −RT ln K
This connects thermodynamics to equilibrium (see the Equilibrium glossary entry and the Reaction rates guide) and to electrochemistry (ΔG° = −nFE°, see the Electrochemistry guide).
05 · Hess's law
Hess's law: calculating unmeasurable enthalpies
Enthalpy is a state function — its value depends only on the current state of the system, not the path taken to get there. This means enthalpy changes are additive: you can combine known reactions to calculate the enthalpy of a reaction that is difficult or impossible to measure directly.
Worked example: Calculate ΔH for C(s) + ½O₂(g) → CO(g) (difficult to measure directly — CO₂ is always produced as a byproduct).
(1) C(s) + O₂(g) → CO₂(g) ΔH₁ = −393.5 kJ/mol
(2) CO(g) + ½O₂(g) → CO₂(g) ΔH₂ = −283.0 kJ/mol
Target = (1) − (2): ΔH = −393.5 − (−283.0) = −110.5 kJ/mol
Hess's law is used in every Born–Haber cycle (lattice enthalpy calculation) and in calculating enthalpies of hydrogenation, combustion, and neutralisation from formation data. See Balancing equations for the stoichiometric manipulation needed.
Thermodynamics — common questions
- Temperature measures average kinetic energy per particle. Heat (q) is the flow of energy from higher to lower temperature. The relationship is q = mcΔT for a substance with specific heat capacity c. An important distinction: heat is a process (energy in transit), not a property stored in a substance.
- ΔG = ΔH − TΔS. When ΔG < 0, the process is thermodynamically spontaneous (the forward reaction is favoured). When ΔG = 0, the system is at equilibrium. ΔG tells you nothing about rate — diamond converting to graphite is spontaneous (ΔG < 0) but has an enormous activation energy and proceeds imperceptibly slowly. See activation energy.
- Entropy is related to the number of microstates (Ω) by Boltzmann's equation S = k ln Ω. Processes that increase the number of particles in the gas phase, dissolve a solid, or mix two substances all increase entropy. The universe's entropy always increases — this is why heat flows from hot to cold, and why you can't unscramble an egg.
- Hess's law follows from enthalpy being a state function (path-independent). To apply it: write the target equation, manipulate known equations (reverse if needed, multiply by stoichiometric factors), and add their ΔH values. Connects to balancing equations and standard enthalpies of formation from the NIST WebBook.
- Exothermic: ΔH < 0, heat released, products at lower energy. Endothermic: ΔH > 0, heat absorbed, products at higher energy. Note: an exothermic reaction can still be non-spontaneous if the entropy change is sufficiently negative (ΔG = ΔH − TΔS > 0). See also activation energy for the energy profile diagram.