Solid metals can be modeled as a set of uncoupled harmonic oscillators of the samefrequency with energy levels given byEn = ħwnn = 0, 1, 2,...where the zero-point energy (the lowest energy state) of each oscillator has been adjustedto zero for simplicity. In this model, the harmonic oscillators represent the motions of themetal atoms relative to one another. The frequency of these oscillators is low so thatħw= = 224KBand the system vibrational partition function is given by3NZ² = la₁ -(11e-0/T).(a) If the system contains one mole of atoms, find the average energy (in J) of this system atT= 172 K. (You can use =BkB.)T(b) What is the absolute entropy (in J/K) for this system? You can use either the Gibbsexpression for S, or the system partition function to make this evaluation (they areequivalent, as your reading assignment indicates).

Solid metals can be modeled as a set of uncoupled harmonic oscillators of the same frequency with energy levels given by En = hwn = 0, 1, 2, ... where the zero-point energy (the lowest energy state) of each oscillator has been adjusted to zero for simplicity. In this model, the harmonic oscillators represent the motions of the metal atoms relative to one another. The frequency of these oscillators is low so that ✪ n = ħw KB and the system vibrational partition function is given by 3N = = 224 1 (1 - e O/T (a) If the system contains one mole of atoms, find the average energy (in J) of this system at Ⓒ T= 172 K. (You can use = = pkB.) T (b) What is the absolute entropy (in J/K) for this system? You can use either the Gibbs expression for S, or the system partition function to make this evaluation (they are equivalent, as your reading assignment indicates).

Solid metals can be modeled as a set of uncoupled harmonic oscillators of the same frequency with energy levels given by En = hwn = 0, 1, 2, ... where the zero-point energy (the lowest energy state) of each oscillator has been adjusted to zero for simplicity. In this model, the harmonic oscillators represent the motions of the metal atoms relative to one another. The frequency of these oscillators is low so that ✪ n = ħw KB and the system vibrational partition function is given by 3N = = 224 1 (1 - e O/T (a) If the system contains one mole of atoms, find the average energy (in J) of this system at Ⓒ T= 172 K. (You can use = = pkB.) T (b) What is the absolute entropy (in J/K) for this system? You can use either the Gibbs expression for S, or the system partition function to make this evaluation (they are equivalent, as your reading assignment indicates).