MASS TRANSFER 249
whenBis not undergoing mass transfer, oruBD0, then:
RTdCA/dy
DFABCBN^0 A
N^0 AD
RT
FABCB
dCA
dy
D
RT
FABCT
CT
CB
dCA
dy
By comparison with Stefan’s Law:
N^0 ADDAB
CT
CB
dCA
dy
(equation 10.29)
Then: DABDRT/FABCT
or: FABD
RT
DABCT
Applying toAin a mixture ofBandC:
dPA/dyDFABCACBuAuB CFACCACCuAuC
For the case whereuBDuCD0:
RT
dCA
dy
D
RT
DABCT
CBN^0 AC
RT
DACCT
CCN^0 A
or: N^0 AD
dCA/dy
CT
CB/DAB CCC/DAC
i
From Stefan’s Law: N^0 ADD^0
CT
CTCA
dCA
dy
D
dCA/dy
CT
CTCA
/D^0
ii
whereD^0 is the effective diffusivity ofAin the mixture
Comparing equations (i) and (ii):
1
D^0
D
1
DAB
CB
CTCA
C
1
DAC
CC
CTCA
For CO 2 in N 2 : N^0 ADD
CT
CN 2
lm
CCO 2
L
DDð
1
yN 2
lm
ð
CTyCO 2
L
(equation 10.33)
DD 1. 6 ð 10 ^5 m^2 /syN 2
1 D 1. 0 ,yN 2
2 D 0 .75,
∴ yN 2
lmD[ 1 0. 75
/ln 1 / 0. 75
]D 0. 87
yCO 2 D 0. 25 ,CTandLare unknown
Hence: N^0 AD
1. 6 ð 10 ^5
0. 87
ð 0. 25
CT
L
D 4. 6 ð 10 ^6 CT/Lkmol/m^2 s
For CO 2 in a mixture of H 2 and N 2 , the effective diffusivity, derived in the first part
of the problem, is used to giveD^0 :
1
D^0
D
1
3. 5 ð 10 ^5
ð
0. 4
1 0. 35
C
1
1. 6 ð 10 ^5
ð
0. 25
1 0. 35
D 2. 4 ð 10 ^5 m^2 /s