Which physicist is associated with the entropy relation S = k log W?

Which physicist is associated with the entropy relation S = k log W?

• A. J. J. Thomson
• B. Michaelis-Menten kinetics
• C. Neutrinos
• D. Ludwig Boltzmann

Answer: (D)

Entropy in statistical mechanics is tied to how many microscopic ways a system can be arranged without changing what we observe macroscopically. Boltzmann’s form, S = k ln W, says that entropy is proportional to the natural logarithm of W, the number of microstates compatible with the macrostate. The constant k (Boltzmann’s constant) sets the scale and bridges the microscopic world to thermodynamics. The logarithm matters: many microstates raise entropy, but not linearly—doubling the number of configurations increases S by k ln 2, not by k times the new count. This formulation arises most cleanly for systems where all microstates are equally likely (the microcanonical view), linking microscopic multiplicity to macroscopic disorder. It’s the foundational bridge Boltzmann built between microscopic arrangements and the thermodynamic quantity we call entropy. The other names listed aren’t associated with this relation: J. J. Thomson is known for discovering the electron; Michaelis-Menten describes enzyme kinetics; neutrinos are fundamental particles. The physicist tied to S = k ln W is Ludwig Boltzmann.

Entropy in statistical mechanics is tied to how many microscopic ways a system can be arranged without changing what we observe macroscopically. Boltzmann’s form, S = k ln W, says that entropy is proportional to the natural logarithm of W, the number of microstates compatible with the macrostate. The constant k (Boltzmann’s constant) sets the scale and bridges the microscopic world to thermodynamics. The logarithm matters: many microstates raise entropy, but not linearly—doubling the number of configurations increases S by k ln 2, not by k times the new count. This formulation arises most cleanly for systems where all microstates are equally likely (the microcanonical view), linking microscopic multiplicity to macroscopic disorder. It’s the foundational bridge Boltzmann built between microscopic arrangements and the thermodynamic quantity we call entropy. The other names listed aren’t associated with this relation: J. J. Thomson is known for discovering the electron; Michaelis-Menten describes enzyme kinetics; neutrinos are fundamental particles. The physicist tied to S = k ln W is Ludwig Boltzmann.