Page 629 - Bird R.B. Transport phenomena

Problems 609

—) = s7—1 (-—)+н (19D.2-3)

Subtraction then gives for а Ф N
дИ\ _ (дН\ (дН_
= (19D.2-4)

The subscript io means "holding all other mass fractions constant/'
y
(b) The left side of Eq. (E) can be expanded by regarding the enthalpy per unit mass to be a
function of p, T, and the first (N - 1) mass fractions:

'.2-5)

Next, verify that the coefficients of the substantial derivatives can be identified as
(дН\ _ л (sin
д In T) PMy (19D.2-6)

(19D.2-7)

The coefficient of p(Da) /Dt) has already been given in Eq. 19D.2-4.
a
(c) Substitute the coefficients into Eq. 19D.2-5, and Jhen use Eq. 19.1-14 to eliminate
p(Do) /Dt), and verify that (dH/dm ) is the same as (H /M ). The summation on a, which
Q
a
a
a vTmy
goes from 1 to N - 1, now has to be appropriately rewritten as a summation from 0 to N, by
using Eq. (K) of Table 17.8-1 and the fact that l r = 0.
a a
(d) Then combine the results of (a), (b), and (c) with Eq. (E) to get Eq. (F).
19D.3. Gas separation by atmolysis or "sweep diffusion" (Fig. 19D.3). When two gases A and В are
forced to diffuse through a third gas C, there is a tendency of A and В to separate because of
3
the difference in their diffusion rates. This phenomenon was first studied by Hertz, and later
3
by Maier. 4 Benedict and Boas studied the economics of the process particularly with regard
to isotope separation. Keyes and Pigford 6 contributed further to both theory and experiment.
Diffusion tube 4' in
length and 1" in diameter,
packed with glass wool

+ B + C T Г A + B + C
Endl End 2
Feed A + B
Make-up
Separator for С " Separator

Raffinate \ A + B Products \ A + B

Fig. 19D.3. The Keyes-Pigford experiment for studying atmolysis.

3
G. Hertz, Zeits.f. Phys., 91, 810-815 (1934).
4 G. G. Maier, Mechanical Concentration of Gases, U.S. Bureau of Mines Bulletin 431 (1940).
5 M. Benedict and A. Boas, Chem. Eng. Prog., 47, 51^62,111-122 (1951).
6 J. J. Keys, Jr., and R. L. Pigford, Chem. Eng. Sci., 6, 215-226 (1957).