In statistic thermodynamics, we can use the partition function to calculate the thermody- namics properties of a system when the system is in thermodynamic equilibrium . For a two level system with energy 1 = -0.01ev and 2 = 0.01 ev consists of No non-interacting particles in contact with a temperature reservoir, consider the following particle distributions: (a) A totally ordered distribution. All particles are in level 1: n1 = No and n2 = 0. Given that: F = U-TS S = klnQ Calculate the per particle Helmholtz energy F/No for this distribution (b) A totally disordered distribution. Particles are evenly distributed in two energy levels: n1 = n2 = No/2. Using Stirling's approximation, express the per particle Helmholtz energy F/No for this distribution as a function of temperature T (c) The equilibrium distribution, where the number of particles in each level and the Helmholtz energy of the system can be calculated from the partition function: No ni P exp KT F = -KT No In P Write down the single particle partition function of the system and use it to express the per particle Helmholtz energy F/No for this distribution as a function of temperature T (d) Use you answer in the first three parts, show that the equilibrium distribution will approach the totally ordered distribution at low temperature limit T - 0 and will approach the totally disordered distribution at high temperature limit Too