Question

Please explain as detail as possible.

a. Explain the assumptions used when formulating heat capacity based on classical theory, Einstein's model and Debye's model!

b. Under what conditions the three theories / models of heat capacity formulation give the same results?

c. Describe how the influence of the types of chemical bonds on condensed materials on their mechanical and electrical properties!

d. Explain how the mechanism of electron transport in metal!

Answer 1

Assumptions of classical theory:

The classical theory now assumes that each atom is a classical three dimensional harmonic oscillator which vibrates independently of all other atoms in the crystal that is the atoms of the crystal behave like independent classical harmonic oscillator.

Assumptions of Einstein model:

1. All atoms are again considerd indentical independent harmonic oscillators as in classical theory.

2. All the oscillators have same natural frequency because of their assumed identical surroundings

3. The energy spectrum of oscillators is not continuous but discrete.

Assumptions of debye model:

In debye model the vibrations are assumed not to be independent of one another because the atoms are bound together by solid state forces but the energies are quantized.

B) At low temperature the three theories give the same results

D) The basic mechanism of electronic transport in metal is given by drude model, which states that

1. Electrons are treated as classical particles within a free-electron approximation. Thus, in the absence of external electromagnetic fields each electron is taken to move uniformly in a straight, line neglecting the interactions with other electrons and ions.

2. Electrons move free only between collisions with scattering centers. Collisions, as in kinetic theory, are instantaneous events that abruptly alter the velocity of an electron.

3. An electron experiences a collision, resulting in an abrupt change in its velocity, with a probability per unit time 1/τ. This implies that the probability of an electron undergoing a collision inany infinitesimal time interval of length dt is just dt/τ.
4. Electrons are assumed to achieve thermal equilibrium with their surroundings only through collisions.