Physical Chemistry Third Edition

1184 28 The Structure of Solids, Liquids, and Polymers

http://www.superconductors.org. It was reported on this site in 2007 that the highest

transition temperature observed at that time was 138 K.

PROBLEMS

Section 28.4: Electrical Resistance in Solids

28.27Without looking up the value, estimate the resistivity of
copper. Look up the correct value and compare your
estimate to it.

28.28The resistivity of silver at 20◦C is 1.59 microohm cm and
its density is 10.5 g cm−^3. Assume that there is one
conduction electron per atom.
a.Find the value ofτ.
b.Find the mean free path for electrons in silver.
c.Give a simple explanation for the comparison of the
mean free path of electrons in silver and gold (see
Example 28.11).

28.29The resistivity of solid mercury at− 39. 2 ◦C is equal to

25.5 microohm cm, and that of liquid mercury at

− 36. 1 ◦C is equal to 80.6 microohm cm. Give a

qualitative explanation for this behavior.

28.30a.Assume that an electric field can be instantaneously

turned off. Estimate the length of time for a

current to drop to 1/eof its initial value when an

electric field is instantaneously turned off in gold

at 20◦C.

b.A current has been flowing in a superconducting

ring since about 1940, without an applied electric

field. Estimate a minimum value of the

conductivity.

28.5 The Structure of Liquids

When a solid melts to form a liquid, its lattice structure suddenly collapses, although

vestiges of this structure remain. The molar volume of most substances increases by

5% to 15%, although that of water decreases by about 8%. In monatomic solids such as

argon each atom has 12 nearest neighbors. When the solid melts, the average number

of nearest neighbors drops from 12 to a value between 10 and 11. In liquids there are

generally numerous small vacant spaces that move around and change their sizes as

the nearest neighbor molecules move. When this disorder is passed on to additional

“shells” of nearest neighbors, next-nearest neighbors, and so on, the long-range order

of the solid is absent.

The Classical Statistical Mechanics Approach

to Liquid Structure

Many of the equilibrium properties of such systems can be obtained through the two-

body reduced coordinate distribution function and the radial distribution function,

defined in Eqs. (27.6-5) and (27.6-7). There are a number of theories that are used

to calculate approximate radial distribution functions for liquids, using classical sta-

tistical mechanics.^22 Some of the theories involve approximate integral equations.

Others are “perturbation” theories similar to quantum mechanical perturbation theory

(see Section 19.3). These theories take a hard-sphere fluid or other fluid with purely

repulsive forces as a zero-order system and consider the attractive part of the forces to

be a perturbation.^23

(^22) H. L. Friedman,A Course in Statistical Mechanics, Prentice-Hall, Englewood Cliffs, NJ, 1985, Chs. 7,
8, and 9; D. A. McQuarrie,Statistical Mechanics, Harper & Row, New York, 1976, Chs. 13 and 14.
(^23) See for example P. J. Camp,Phys. Rev. E, 67 , 11503 (2003).