Page 303 - Bird R.B. Transport phenomena

Problems 287

9A.1 Prediction of thermal conductivities of gases at 9A.3. Estimation of the thermal conductivity of a dense
low density. gas. Predict the thermal conductivity of methane at 110.4
(a) Compute the thermal conductivity of argon at 100°C atm and 127°F by the following methods:
and atmospheric pressure, using the Chapman-Enskog (a) Use Fig. 9.2-1. Obtain the necessary critical properties
theory and the Lennard-Jones constants derived from vis- from Appendix E.
cosity data. Compare your result with the observed value 1 (b) Use the Eucken formula to get the thermal conductiv-
7
of506xKT cal/cm-s-K. ity at 127°F and low pressure. Then apply a pressure cor-
(b) Compute the thermal conductivities of NO and CH at rection by using Fig. 9.2-1. The experimental value 2 is
4
300K and atmospheric pressure from the following data 0.0282 Btu/hr- ft -F.
for these conditions: Answer: (a) 0.0294 Btu/hr • ft • F.
7
fju X 10 (g/cm • s) C (cal/g-mole • K) 9A.4. Prediction of the thermal conductivity of a gas
p
mixture. Calculate the thermal conductivity of a mixture
1929 7.15
containing 20 mole % CO and 80 mole % H at 1 atm
2 2
CH 4 1116 8.55 and 300K. Use the data of Problem 9A.2 for your cal-
culations.
Compare your results with the experimental values given Answer: 2850 X 10 cal/cm • s • К
7
in Table 9.1-1.
9A.5. Estimation of the thermal conductivity of a pure
9A.2 Computation of the Prandtl numbers for gases at liquid. Predict the thermal conductivity of liquid H O at
low density. 2 6
40°C and 40 megabars pressure (1 megabar = 10
(a) By using the Eucken formula and experimental heat dyn/cm ). The isothermal compressibility, (l/p)(dp/dp) ,
2
T
capacity data, estimate the Prandtl number at 1 atm and is 38 X 10~ 6 megabar 1 and the density is 0.9938 g/cm .
3
300K for each of the gases listed in the table. Assume that C p = C . v
(b) For the same gases, compute the Prandtl number di- Answer: 0.375 Btu/hr • ft • F
rectly by substituting the following values of the physical
properties into the defining formula Pr = С /л/к, and com- 9A.6. Calculation of the Lorenz number.
р
pare the values with the results obtained in (a). All proper- (a) Application of kinetic theory to the "electron gas" in a
3
ties are given at low pressure and 300K. metal gives for the Lorenz number
C X 1СГ 3 /i, X 10 5 к L = (9A.6-1)
p
Gas" J/kg-K Pa°s W/m-К
in which к is the Boltzmann constant and e is the charge
He 5.193 1.995 0.1546 on the electron. Compute L in the units given under
Ar 0.5204 2.278 0.01784 Eq. 9.5-1.
H 2 14.28 0.8944 0.1789 (b) The electrical resistivity, 1 /k , of copper at 20°C is
e
Air 1.001 1.854 0.02614 1.72X 10~ 6 ohm • cm. Estimate its thermal conduc-
CO 2 0.8484 1.506 0.01661 tivity in W/m • К using Eq. 9A.6-1, and compare
H O 1.864 1.041 0.02250 your result with the experimental value given in
2
Table 9.1-4.
" The entries in this table were prepared Answers: (a) 2.44 X 10~ volt /K ; (b) 416 W/m • К
8
2
2
from functions provided by Т. Е. Daubert,
R. P.Danner, H. M. Sibul, С. С Stebbins, 9A.7c Corroboration of the Wiedemann-Franz-Lorenz
J. L. Oscarson, R. L. Rowley, W. V. Wilding, law. Given the following experimental data at 20°C for
M. E. Adams, T. L. Marshall, and N. A. Zundel, pure metals, compute the corresponding values of the
DIPPR ® Data Compilation of Pure Compound
Properties, Design Institute for Physical Property Lorenz number, L, defined in Eq. 9.5-1.
Data®, AIChE, New York (2000).
J. M. Lenoir, W. A. Junk, and E. W. Comings, Chem. Engr.
2
Prog., 49, 539-542 (1953).
1 3
W. G. Kannuluik and E. H. Carman, Proc. Phys. Soc. J. E. Mayer and M. G. Mayer, Statistical Mechanics, Wiley,
(London), 65B, 701-704 (1952). New York (1946), p. 412; P. Drude, Ann. Phys., 1, 566-613 (1900).