Worked example: Estimate the Debye temperature's meaning — for lead, Θ_D = 105 K. At what temperature do 'all' phonon modes become active, and what is the corresponding maximum phonon energy? Step 1: By definition k_B·Θ_D = ℏω_D, the maximum phonon energy: E_max = k_B × 105 K. Step 2: E_max = 1.381×10⁻²³ × 105 = 1.45×10⁻²¹ J = 9.05 meV. Step 3: Compare with room-temperature thermal energy k_B·300 K = 25.9 meV > 9.05 meV — at 300 K all lead phonon modes are excited, so its heat capacity has saturated at the Dulong–Petit value 3R. Step 4: For diamond Θ_D = 2230 K: at 300 K only a fraction of modes are active, so diamond's heat capacity is far below 3R — hard crystals need high temperatures to 'thaw' their stiff vibrations. Conclusion: Θ_D measures lattice stiffness — soft lead saturates early, stiff diamond stays quantum-frozen at room temperature.