Teaching Entropy from Phase Space Perspective: Connecting the Statistical and Thermodynamic Views Using a Simple One-Dimensional Model

Connecting the thermodynamic definition of entropy, dS = dQ/T (Clausius’s equation), with the statistical definition, S = kB ln Ω (Boltzmann’s equation), has been a persistent challenge in chemical education at the undergraduate level. Not meeting this challenge results in students taking away the meaning of entropy in a vague and subjective way as a measure of “disorder” or increase in number of configurations without any meaningful way of connecting it to heat. To address this challenge, we present a simple model that connects these two definitions. This approach relies centrally on emphasizing that the number of configurations, Ω, includes configurations in both real space and momentum space, collectively known as the phase space. Without including momentum configurations (i.e., how fast the particles move), connecting heat to entropy change is not possible. We construct the phase space for an ensemble of simple one-dimensional systems at equilibrium and show that delivery of heat dQ to the system resu...