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Unit 9

Entropy and free energy

A cold pack absorbs heat yet runs by itself, limestone needs more than 800 °C to decompose, and iron can be smelted with charcoal while aluminium cannot. What decides the direction of a change is not energy alone but entropy — the number of ways energy can be shared out. This unit starts by counting microstates and ends with Gibbs energy, equilibrium constants and the Ellingham diagrams of metallurgy.

6 lessons ≈ 185 min 0 of 6 lessons complete

  1. 1 Entropy: counting the ways Why does heat always flow from hot to cold? Because that way of sharing energy has unimaginably more arrangements. Start from the microstates of Einstein solids, understand S = k ln W, then compute entropy changes of phase changes, mixing and reactions. 30 min
  2. 2 Entropy and heat capacity from molecular levels N₂ and CO weigh the same, yet CO has 6 J K⁻¹ mol⁻¹ more entropy. Partition functions split the entropy into translation, rotation and vibration, reproduce the tabulated standard entropies from spectroscopic constants, and show heat capacity rising as vibration wakes up. 35 min
  3. 3 Heat capacity of solids and third-law entropy Why does a mole of metal atoms hold about 25 J/K while diamond holds a quarter of that? Start from the Dulong–Petit law and atomic masses by the method of mixtures, fit Einstein’s quantised vibrations to the diamond data, then integrate copper’s low-temperature heat capacity from 0 K to its standard entropy. 35 min
  4. 4 Gibbs energy: temperature decides Count the surroundings’ entropy too and out comes ΔG = ΔH − TΔS. Four sign cases, one ΔH–ΔS map and a temperature slider explain why water freezes below 0 °C and limestone needs a hot kiln. 25 min
  5. 5 Free energy and equilibrium ΔG° = −RT ln K: one table of thermodynamic data yields the equilibrium constant of ammonia synthesis, the ionic product of water and the solubility product of silver chloride. The van ’t Hoff equation says how K moves with temperature; comparing Q with K says which way a reaction goes. 30 min
  6. 6 Ellingham diagrams and metal extraction Plot each metal oxide’s ΔG° as a straight line against temperature and you have the metallurgist’s map: who can reduce whom, how hot it must be, and what happens inside a blast furnace. 30 min