Page 305 - Bird R.B. Transport phenomena

Problems 289

mated as oblate spheroids, with an axis ratio of 4, for These three equations give the density corrections to the
which g! = g 2 = 0.144; g 3 = 0.712. viscosity and thermal conductivity of a hypothetical gas
Answer: (a) From Eq. 9.6-4, 4.93 X 10" 3 cal/cm • s • К made up of rigid spheres.
3
(spherical), and 6.22 X 10~ cal/cm • s • K. From Eq. 9.6-1, Enskog further suggested that for real gases, (i) у can
3
5.0 X 10~ cal/cm-s-K be given empirically by
9A.12. Calculation of molecular diameters from trans-
port properties. (9C.1-4)
(a) Determine the molecular diameter d for argon from Eq. where experimental p-V-T data are used, and (ii) b can be
0
1.4-9 and the experimental viscosity given in Problem 9A.2. determined by fitting the minimum in the curve of
(b) Repeat part (a), but using Eq. 9.3-12 and the measured (/x //л ) V versus y.
0
thermal conductivity in Problem 9A.2. Compare this result (a) A useful way to summarize the equation of state is to
with the value obtained in (a). use the corresponding-states presentation 8 of Z = Z(p ,
(c) Calculate and compare the values of the Lennard-Jones T ), where Z = pV/RT, p = p/p , and T = T/T . Show r
r
c
r
c
r
collision diameter a from the same experimental data used that the quantity у defined by Eq. 9C.1-4 can be com-
in (a) and (b), using е/к = 124K. puted as a function of the reduced pressure and tempera-
(d) What can be concluded from the above calculations? ture from
Answer: (a) 2.95 A; (b) 1.88 A; (c) 3.415 A from Eq. 1.4-14, 1 + (Лп Z/dln T )
3.425 A from Eq. 9.3-13 r Pr (9C.1-5)
1 - (d\n Z/dln p ) r Tr
9C.1. Enskog theory for dense gases. Enskog 7 devel-
oped a kinetic theory for the transport properties of dense (b) Show how Eqs. 9C.1-1, 2, and 5, together with the
gases. He showed that for molecules that are idealized as Hougen-Watson Z-chart and the Uyehara-Watson /т//л с
rigid spheres of diameter a 0 chart in Fig. 1.3-1, can be used to develop a chart of k/k as
c
a function of p r and T . What would be the limitations of
r
— ^ = 1 + 0.8 0.761y (9C.1-1) the resulting chart? Such a procedure (but using specific
o
fi й 0 if p-V-T data instead of the Hougen-Watson Z-chart) was
(9C.1-2) used by Comings and Nathan. 9
(c) How might one use the Redlich and Kwong 10 equation
Here JJL° and k° are the low-pressure properties (computed, of state
for example, from Eqs. 1.4-14 and 9.3-13), V is the molar
volume, and b 0 = ^TTNOQ, where N is Avogadro's number. (V -b) = RT (9C.1-6)
The quantity у is related to the equation of state of a gas of VTviv + b)J
rigid spheres: for the same purpose? The quantities a and b are constants
characteristic of each gas.
^ ) + 0.2869^?Y + • • •
RT
(9С.1-3)
8
O. A. Hougen and К. М. Watson, Chemical Process
Principles, Vol. II, Wiley, New York (1947), p. 489.
D. Enskog, Kungliga Svenska Vetenskapsakademiens E. W. Comings and M. F. Nathan, Ind. Eng. Chem., 39,
7 9
Handlingar, 62, No. 4 (1922), in German. See also J. O. Hirschfelder, 964-970 (1947).
C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, 10 O. Redlich and J. N. S. Kwong, Chem. Rev., 44, 233-244
2nd printing with corrections (1964), pp. 647-652. (1949).