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Debye model
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Phonons explain low-temperature heat capacity.
C ∝ T³Treats lattice vibrations as quantised sound waves (phonons) with a cutoff frequency. It predicts C ∝ T³ at low temperature.
Matches measurements of insulators near 10 K.
Electrons add a linear term in metals.
In more detail
The Debye model explains the specific heat of solids at low temperatures, predicting that it rises with the cube of temperature. It treats atomic vibrations as sound waves with a maximum frequency.
Real-world uses
- Materials scientists use the Debye model to estimate thermal properties.
- Low-temperature physics uses it to interpret heat capacity data.
- Physicists use the Debye model to predict how heat capacities of solids drop at low temperatures.
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Frequently asked questions
What is the Debye temperature?
A characteristic temperature that marks where quantum effects become important for vibrations.
Why does heat capacity drop at low temperature?
Because fewer vibrational modes are excited when energy is low.
Why does the heat capacity fall at low temperature?
Quantum vibrations freeze out, so only the lowest-energy vibrations can store heat.
Related topics in Kinetic Theory & Statistical Physics
Bose–Einstein condensate · Fermi energy · Specific heat of solids · Photon gas · Planck distribution · Random walks