CHEMICAL ENGINEERING

256 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

It may be noted that:

∫ 1

0

ex

2

dxD

p



2

Solution

(a) If the age distribution function be ft
, then the surface in the age groupttotCdt
is: ft
dt.
Then, the surface of agetCdt
minus, the surface of agetCdt
is the surface
destroyed in the dt,or:

ft

ftCdt

Dsft

dt

or: f^0 tCdt
dtDsft
dt

As dt!0, f^0 t
Csft
D 0 i

Using the integrating factor e

∫

sdtDestthen:

estft

DK(const)

and: ft
DKest ii

the total surfaceD 1 DK

∫ 1

0

estdtDK

[

est

s

] 1

0

D

K

s

and hence: ft
Dsest

The mass transfer rate into fraction of surface of agettotCdt(per unit total area of
surface) is: √
D
t

CAsestdtD

√

D



CAestt^1 /^2 dt

The mass transfer rate per unit area,

NAD

√

D



CA

∫ 1

0

t^1 /^2 estdt

PuttingstDˇ^2 : sdtD 2 ˇdˇ

and: NAD

√

D



CA

∫ 1

0

s^1 /^2

ˇ

eˇ

2

2 ˇdˇ

D 2

√

sD



CA

∫ 1

0

eˇ

2

dˇ

D 2

√

sD



CA

p



2

D

p

DsCA iii

Thus: the mass transfer coefficientD

NA

CA

D

p

Ds