Question

1-Explain specific features of Einstein and Debye models for the specific heat.

2-Recall the Fermi-Dirac distribution.

3-Recall the expression for electron density of states of electron gas.

Answer 1

1. according to einstien's theorey of specific heat, the specific heat approaches zero exponentially fast at low temperatures. This is because all the oscillations have one common frequency.

but according to debye;s model, ittreats the vibrations of the atomic lattice (heat) as phonons in a box, in contrast to the Einstein model, which treats the solid as many individual, non-interacting quantum harmonic oscillators. The Debye model correctly predicts the low temperature dependence of the heat capacity, which is proportional to T^3

2. Fermi dirac distributions describe a distribution of particles over energy states in systems consisting of many identical particles that obey the Pauli exclusion principle.

ni = (e^(ei - mu)/kT + 1)^-1

where k is boltzmann's constnat

T is absolute temperature

ei is energy of the single particle state i

mu is the total chemical potential

ni is the average number of fermions in a single particle state i

3. According to the free electron model

the density of states (number of energy states, per energy per volume) of a non-interacting electron gas is given by:

g(E) = me*sqrt(2me*E)/pi^2*h^3

where h is reduced planks constant

me is mass of electron

E is energy of electron