Entropy

The first law explains how much energy is conserved, but not why transformations always go in one direction: coffee cools, gas expands into a vacuum, hot and cold bodies move towards equilibrium, but never the reverse. Answering this requires a new quantity, entropy: the measure of the number of microstates compatible with a macrostate, and the compass that orients the arrow of time. This chapter defines it (Boltzmann’s formula), provides the practical formulae for $\Delta S$, states the second law and applies it to heat, free expansion and the maximum extractable work.

Sections

• Microstates, macrostates and ignorance
• Definition of entropy
• Entropy change for the most common systems
• The second law of thermodynamics
• The reversible cooling of coffee

Reflections

• The arrow of time
• The arrow of time: why the past differs from the future

Exercises

• All the worked exercises in the chapter