Blundell Thermal Physics · Problem 34.4

Non-equilibrium thermodynamics

Physics — Statistical Mechanics · thermopower-entropy-per-carrier

Problem

(a) Explain why the thermopower is a measure of the entropy per carrier. (b) Consider a classical gas of charged particles and explain why the thermopower

\epsilon

should be of the order of

k_\mathrm{B}/e = 87~\mu\mathrm{V\,K}^{-1}

and be independent of temperature

T

. (c) In a metal, the measured thermopower is much less than

87~\mu\mathrm{V\,K}^{-1}

and decreases as the metal is cooled. Give an argument for why one might expect the thermopower to behave as

\epsilon \approx \frac{k_\mathrm{B}}{e}\frac{k_\mathrm{B}T}{T_\mathrm{F}},\tag{34.69}

where

T_\mathrm{F}

is the Fermi temperature. (d) In a semiconductor, the measured thermopower is much larger than

87~\mu\mathrm{V\,K}^{-1}

and increases as the metal is cooled. Give an argument for why one might expect the thermopower to behave as

\epsilon \approx \frac{k_\mathrm{B}}{e}\frac{E_\mathrm{g}}{2k_\mathrm{B}T},\tag{34.70}

where

E_\mathrm{g}

is the energy gap of the semiconductor. (e) Since thermopower is a function of the entropy of the carriers, the third law of thermodynamics leads one to expect that it should go to zero as

T \to 0

. Is this a problem for the semiconductor considered in (d)?

Related theory

Quantum Entropy And Von Neumann Entropy

Browse the problem library