A system comprised of 3 non-interacting particles has 4 one-particle states (call them 1, 2, 3, and 4). How must these particles be placed in these one-particle states taking their statistics into account? In other words, list the probable thermodynamic states of the system. For each part, also state which thermodynamic states are important in the classical regime. a) distinguishable particles (call them A, B, C), that is, those particles subject to classical statistics, b) identical bosons (call them A), c) identical fermions (call them A). What is the number of thermodynamic states in each case?

Problem Consider the ODE x = 2-3x with initial condition x(to) = 1 and to = 0. What is the value of the state x when t = 2? Estimate when the system will decay to a constant value using the time constant of the system (i.e., after 4 time constants)? 4

Problem 1: Consider a classical ideal gas in three dimensions, with N indistinguishable atoms confined in a box of volume N³. Assume the atoms have zero spin and neglect any internal degrees of freedom. Starting from the energy levels of a single atom in a box, find: (a) The Helmholtz free energy F' Hint: ſ. -ax² d.x e Va (b) The entropy o (c) The pressure p

calculate the heat capacity of an Einstein solid in the low-temperature limit. Sketch the predicted heat capacity as a function of temperature. (Note: Measurements of heat capacities of actual solids at low temperatures do not confirm the prediction that you will make in this problem.