Chapter 17 - Thermodynamics: Entropy, Free Energy and Equilibrium - Section Problems - Page 750: 53

$1.27\times10^{-20}\,J/K$

Number of ways $W=B^{N}=10000^{100}=(10^{4})^{100}=10^{400}$ $S=k\ln W$ where the Boltzmann constant $k=1.38\times10^{-23}\,J/K$ Then $S=(1.38\times10^{-23}\,J/K)\times \ln (10^{400})$ $=1.27\times10^{-20}\,J/K$