Page 296 - Bird R.B. Transport phenomena

280 Chapter 9 Thermal Conductivity and the Mechanisms of Energy Transport

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EXAMPLE 9.4-1 The density of liquid CC1 at 20°C and 1 atm is 1.595 g/cm , and its isothermal compressibility
4
1
6
{1/р){др/др) is 90.7 X 10" atm" . What is its thermal conductivity?
Prediction of the т
Thermal Conductivity SOLUTION
of a Liquid
First compute
dp 1 1 = 6.91 X 10 atm • cm /g
3
3
6
р(1/р)(др/др) (1.595X90.7 X 1(Г )
др 1т т
9
2
2
= 7.00 X 10 cm /s (using Appendix F) (9.4-5)
Assuming that C /C = 1.0, we get from Eq. 9.4-4
p v
4
9
v s = V(l.0X7.00 X 10 ) = 8.37 X 10 cm/s (9.4-6)
The molar volume is V = M/p = 153.84/1.595 = 96.5 cm /g-mole. Substitution of these val-
3
ues in Eq. 9.4-3 gives
2/3
= 2.S0(N/V) Kv,
/б.О23 x 10 V , 16 4
23
/3
= 2 8( (1.3805 X 10" )(8.37X 10 )
0.965 X 10 2
ч
2
4
= 1.10 x 10 (cm- )(erg/K)(cm/s)
= 0.110W/m-K (9.4-7)
The experimental value given in Table 9.1-2 is 0.103 W/m • K.
§9«5 THERMAL CONDUCTIVITY OF SOLIDS
Thermal conductivities of solids have to be measured experimentally, since they depend
on many factors that are difficult to measure or predict. 1 In crystalline materials, the
phase and crystallite size are important; in amorphous solids the degree of molecular
orientation has a considerable effect. In porous solids, the thermal conductivity is
strongly dependent on the void fraction, the pore size, and the fluid contained in the
pores. A detailed discussion of thermal conductivity of solids has been given by Jakob. 2
In general, metals are better heat conductors than nonmetals, and crystalline materi-
als conduct heat more readily than amorphous materials. Dry porous solids are very
poor heat conductors and are therefore excellent for thermal insulation. The conductivi-
ties of most pure metals decrease with increasing temperature, whereas the conductivi-
ties of nonmetals increase; alloys show intermediate behavior. Perhaps the most useful
of the rules of thumb is that thermal and electrical conductivity go hand in hand.
For pure metals, as opposed to alloys, the thermal conductivity к and the electrical
conductivity k are related approximately 3 as follows:
e
= L = constant (9.5-1)
kJ
This is the Wiedemann-Franz-Lorenz equation; this equation can also be explained theoret-
9
2
ically (see Problem 9A.6). The "Lorenz number" L is about 22 to 29 X 1СГ volt /K 2 for

1 A. Goldsmith, T. E. Waterman, and H. J. Hirschhorn, eds., Handbook of Thermophysical Properties of
Solids, Macmillan, New York (1961).
2 M. Jakob, Heat Transfer, Vol. 1, Wiley, New York (1949), Chapter 6. See also W. H. Rohsenow,
J. P. Hartnett, and Y. I. Cho, eds., Handbook of Heat Transfer, McGraw-Hill, New York (1998).
3 G. Wiedemann and R. Franz, Ann. Phys. u. Chemie, 89, 497-531 (1853); L. Lorenz, Poggendorff's
Annalen, 147,429-452 (1872).