Classical thermodynamics of a two-state system: a (very small) discrete system has

Classical thermodynamics of a two-state system: a (very small) discrete system has only two states l and 2 with energies el =-eo and e2-eo, respectively. this could, for instance, be a spin 1/2 particle in an external magnetic field. since this system contains only one particle, the different thermodynamic ensembles (of the systems described below) do not provide equivalent descriptions of the physics. we want to explore this difference for this simplest possible system. (a) if the system is isolated from the environment which are the possible values for the internal energy of the system? [5 points] (b) in the following we assume that the system is not isolated any more but instead interacting with a heat bath of temperature t. using the canonical distribution of classical thermodynamics, what are the probabilities p, to find the system in each of the two states in this case? [10 points] (c) find the internal energy as a function of the temperature of the heat bath (express it in terms of a familiar hyperbolic function). [15 points] (d) using the limiting values of the expression in (c), what are the possible values for the internal energy of the system when coupled to the heat bath? [10 points]