Problem 3: Harmonic oscillator. Canonical ensemble. Consider a system of N harmonic oscillators. We assume that the oscillators are distinguishable, one-dimensional, practically independent and having the same angular frequency w. 1) Compute the partition function Z, for one subsystem (i.e. harmonic ocilator). 2) Compute the partition function Z for the system. 3) Deduce the free energy. 4) Deduce the entropy. 5) Deduce the internal energy.

Problem 3: Harmonic oscillator. Canonical ensemble. Consider a system of N harmonic oscillators. We assume that the oscillators are distinguishable, one-dimensional, practically independent and having the same angular frequency w. 1) Compute the partition function Z, for one subsystem (i.e. harmonic ocilator). 2) Compute the partition function Z for the system. 3) Deduce the free energy. 4) Deduce the entropy. 5) Deduce the internal energy.