In thermodynamics

Thermodynamics

Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

 and solid state physics, the Debye model is a method developed by Peter Debye

Peter Debye

Peter Joseph William Debye FRS was a Dutch physicist and physical chemist, and Nobel laureate in Chemistry.-Early life:...

 in 1912 for estimating the phonon

Phonon

In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...

 contribution to the specific heat (heat capacity) in a solid

Solid

Solid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...

. It treats the vibration

Oscillation

Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...

s of the atomic lattice (heat) as phonon

Phonon

In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...

s in a box, in contrast to the Einstein model

Einstein solid

The Einstein solid is a model of a solid based on two assumptions:* Each atom in the lattice is an independent 3D quantum harmonic oscillator* All atoms oscillate with the same frequency...

, which treats the solid as many individual, non-interactingquantum harmonic oscillator

Quantum harmonic oscillator

The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics...

s. The Debye model correctly predicts the low temperature dependence of the heat capacity, which is proportional to – the Debye T³ law.