Consider a system of N identical but distinguishable particles, which can occupy either of two energy levels: &o = 0 or

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Consider A System Of N Identical But Distinguishable Particles Which Can Occupy Either Of Two Energy Levels O 0 Or 1 (362.5 KiB) Viewed 200 times

Consider a system of N identical but distinguishable particles, which can occupy either of two energy levels: &o = 0 or &₁ = ε > 0. The upper energy level (ε₁ = ɛ) is g-fold degenerate. The total energy of the system is E. a) Using the microcanonical ensemble, show that the number of microstates with total energy E is Ω(Ε,Ν) N!g"+ n_!(N-n_)! where n+ = E/e corresponds to the number of particles with energy &. b) Explain why the state-counting correction used in the ideal gas is not necessary. c) Find the entropy S(E, N), applying the Stirling approximation for large N. d) Express n as a function of the temperature of the system.