Thermal Physics - Einstein solid

One feature common to both the Debye theory and the Einstein theory of the specific heat of a crystal composed of N identical atoms is that the

1. Average energy of each atom is 3kT
2. Vibrational energy of the crystal is equivalent to the energy of 3N independent harmonic oscillators
3. Crystal is assumed to be continuous for all elastic waves
4. Speed of the longitudinal elastic waves is less than the speed of the transverse elastic waves
5. Upper cutoff frequency of the elastic waves is the same

(GR8677 #51)

Solution:

Einstein solid:

• Thermal properties of crystal
• Highly idealized model focusing only the vibrational modes of crystal
• Assumption: Each of N atoms is free to vibrate around its equilibrium position in any of 3 coordinate directions by a harmonic force with a natural frequency ω₀.

Einstein solid equipartition energy:

• Number of oscillator N = N₀,
• 3-D Harmonic Oscillator, f = 6
• U = (6/2) N₀kT = 3N₀kT

Answer: B