Reading Response, Week 13 Reading Response - Week 13 Reading Response - Week 13 Last Name, First Name * email * 1: The partition factor associated with the rotation of diatomic molecules is given in eq. (6.30). The energy that goes into the Boltzmann factor is given in eq. (6.29); note that the rotational energy levels are quantized. In eq. (6.30) there is a factor of (2j +1); where did this factor come from? 2: Look at the derivation of the equipartition theorem shown in section 6.3. What parts of this derivation would you like to go over in class? 3: Why does the equipartition theorem fail for quantum mechanical systems at low temperature? 4: Why is the probability finding a molecule at any given speed equal to zero? 5: Eq. (6.45) is essentially the Boltzmann factor, and indicates that the most probable velocity is zero. This makes sense, since for finite positive temperatures, the most probable energy is the lowest energy. For translational kinetic energy, that lowest energy is zero. So why isn't the most probable speed also equal to zero? 6: Consider eq. (6.50), the Maxwell (speed) distribution, which we can consider as consisting of three parts: (i) the part in parenthesis that is raised to the 3/2 power; (ii) the 4πv term; and (iii) the exponential term. What does each term do/correspond to/represent physically? 7: How can you relate the Helmholtz free energy F to the partition factor Z? Why is this formula useful? 8: Eq. (6.70) is the partition function for non-interacting, indistinguishable particles. What does the 1/N! term do? 9: Look over the derivation that leads from eq. (6.75) to eq. (6.82). What would you like to go over in class? What material from this reading (or previous classes) would you like us to go over in more detail? Submit Δ
