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Problem 1: Two-level system. Canonical ensemble.

Problem 1: Two-level system. Canonical ensemble.

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Problem 1: Two-level system. Canonical ensemble. Consider N impurity atoms trapped in a solid matrix. Each impurity can be in one of two states, with energies 0 and ɛ, respectively. The energy level are non-degenerate. 1) Compute the partition function Z, for one subsystem (i.e. one impurity atom). 2) Compute the partition function Z for the system. 3) Deduce the free energy. 4) Deduce the entropy. 5) Deduce the internal energy. Problem 2: Two-level system. Canonical ensemble. Redo the above problem. We assume that the ground level is non degenerate and the excited level is g-fold degenerate.
Transcribed Image Text:Problem 1: Two-level system. Canonical ensemble. Consider N impurity atoms trapped in a solid matrix. Each impurity can be in one of two states, with energies 0 and ɛ, respectively. The energy level are non-degenerate. 1) Compute the partition function Z, for one subsystem (i.e. one impurity atom). 2) Compute the partition function Z for the system. 3) Deduce the free energy. 4) Deduce the entropy. 5) Deduce the internal energy. Problem 2: Two-level system. Canonical ensemble. Redo the above problem. We assume that the ground level is non degenerate and the excited level is g-fold degenerate.
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