Use mathematical software, a spreadsheet, or the Living graphs on the web site for this book to:

(a) Consider a three-level system with levels 0, ε, and 2ε. Plot the partition function against kT/ε.

(b) Plot the function dS/dT for a twolevel system, the temperature coefficient of its entropy, against kT/ε. Is there a temperature at which this coefficient passes through a maximum? If you find a maximum, explain its physical origins.

(c) Plot the temperature dependence of the vibrational contribution to the molecular partition function for several values of the vibrational wavenumber. Estimate from your plots the temperature above which the harmonic oscillator is in the high-temperature limit.