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2. From the differentials for the thermodynamic potentials, derive the Maxwell relations. [20 han 3. A particular atomic level is found to an energy & 27h² Determine its degeneracy. [20] = 8mL 4. The partially complete table below displays the occupation numbers of four equally spaced energy levels of an assembly. The missing data are labelled [A]. . [C], [D] and [E]. Elk 1 2 5 6 3 4 81 4 (A 1 0 1 1 ICIS 0.744 3 0 2 3 0 2 4 1 2 1 0 (B) 4 1 3 3 2.100 1 2 2 1 0 1 0 1 0.822 W₁ 45 50 120 75 (D) 100 (a) Determine the total number of particles in the system. (b) Determine the total energy (in units of e) of the system - if possible. (c) Determine [A]. . [C]. [D] and [E]. (d) Demonstrate that there is no restriction on the distribution of particle in this assembly (e) Demonstrate that this assembly is made up of Bosons and not classical particles (f) Explain why Macrostate 3 has a very high Thermodynamic Probability. (g) Explain why is Macrostate 3 the most probable macrostate. [40] M²ny