This homework assignment covers several topics in thermodynamics and statistical mechanics. It includes 6 problems related to thermal equilibrium of isolated systems (problem 4), deriving the escape velocity of Earth (problem 7), applying the equipartition theorem to model thermal fluctuations in a spring balance (problem 8), and reviewing probability distributions and average energy as a function of temperature (problems 9-10). Key steps are outlined for some problems, such as using a Taylor expansion to approximate a probability distribution as Gaussian near its maximum for problem 4.