Problems and Solutions on Thermodynamics and Statistical Mechanics

Statiaticol Physics 361

the collisions and the transmission of energy will become faster. Hence the
thermal conductivity is higher for greater gas density.

(b) As the air density is low, the thermal conductivity is also low. It
can therefore enhance heat insulation.

2172
Sketch the temperature dependence of the heat conductivity of an in-
sulating solid. State the simple temperature dependencies in limiting tem-
perature ranges and dervie them quantitatively.
(Chicago)
Solution:
The thermal conductivity of a solid is n = cu,X/3, where c is thermal
capacity per unit volume, w, is velocity of sound, X is mean free path of
phonons. n versus T is shown in Fig. 2.37.
(a) At low temperatures the heat capacity c a T3, w, and X are con-
stants, hence K. a T3.
1
T

(b) At high temperatures u, is constant and X a -, the thermal ca-

1

pacity c is constant, hence K. a -.

T

Fig. 2.37. T

2175
Express the equilibrium heat flow equation in terms of the heat capac-
ity, excitation or particle velocity, mean free path, and thermal gradient.
Discuss the manifestation of quantum mechanics and quantum statistics in
the thermal conductivity of a metal.
( wis co nsin)