Fermi estimate: entropy of a burnt book

Problem

Estimate the change in entropy of the universe when a $500\;\text{g}$ book burns completely, producing ash and releasing about $15\;\text{MJ}$ of heat into the air at temperature $T\approx 300\;\text{K}$.

Solution

Setup: in the entropy balance the dominant contribution is the heat $Q$ poured into the air at a nearly constant temperature $T$. The air absorbs $Q$ at $T$, so it gains entropy $\Delta S\approx\frac{Q}{T}=\frac{15\cdot 10^6}{300}=5\cdot 10^4\;\text{J/K}$

The chemical rearrangement paper $\to$ ash involves a configurational entropy change of order $N k_B$ (with $N$ the number of molecules), i.e. at most a few hundred J/K: entirely negligible compared with the thermal term. $\ev{\Delta S_\text{univ}\approx 5\cdot 10^4\;\text{J/K}=50\;\text{kJ/K}}$

Linked atoms

Topics: Entropia e secondo principio Concepts: Entropia Skills: Stime di Fermi · Bilancio entropico