This template explores the implications of the Boltzmann Equation for the population of energy states as a function of temperature. It uses the graphing power of Mathcad to provide a concrete, visual presentation of relative population of the first four vibrational states of carbon monoxide from 0 K to very high temperatures and focuses attention on what happens to the relative populations of these states over that range, especially at the extremes of infinite and zero absolute temperature (Figure 1). It then seeks to increase the user’s understanding of the Boltzmann Equation by exploring the implications of hypothetical negative absolute temperatures and asking the question "Would negative absolute temperature be very hot or very cold?"

Figure 1. The distribution of particles, N, over the first four vibrational energy states of CO as a function of the temperature T. The number of particles in each energy state approaches a constant as the temperature increases.