CHEMICAL ENGINEERING

MASS TRANSFER 283

0. 260 ð 106 C

1

hD

D 0. 312 ð 106 C 0. 792

1

hD

1

hD

D 0. 25 ð 106 and:hDD 4. 0 ð 10 ^6 m/s.

PROBLEM 10.47

Explain the basic concepts underlying the two-film theory for mass transfer across a phase
boundary and obtain an expression for film thickness.
Water evaporates from an open bowl at 349 K at the rate of 4. 11 ð 103 kg/m^2 s. What
is the effective gas-film thickness?
The water is replaced by ethanol at 343 K. What will be its rate of evaporation in
kg/m^2 s if the film thickness is unchanged?
At the surface of the ethanol, what proportion of the total mass transfer will then be
attributable to bulk flow?
Data.

Vapour pressure of water at 349 KD34 mm Hg

Vapour pressure of ethanol at 343 KD544 mm Hg

Neglect the partial pressure of vapour in the surrounding atmosphere

Diffusivity of water vapour in airD 26 ð 10 ^6 m^2 /s

Diffusivity of ethanol in airD 12 ð 10 ^6 m^2 /s

Density of mercuryD 13 ,600 kg/m^3

Universal gas constantRD8314 J/kmol K

Solution

For evaporation for a free surface, Stefan’s law is applicable or:

N^0 ADD

CT

CB

dCT

dy

DCD

CT

CB

dCB

dy

(from equation 10.30)

Integration gives: N^0 AD

D

y 2 y 1

CTln

CB 2

CB 1

D

D

y 2 y 1

CT

CBm

CA 1 CA 2

For water:Vapour pressure,PA 1 D301 mm Hg at 349 K

At 349 K: CA 1 D

PA 1

RT

D

 0. 301 ð 13 , 600 ð 9. 81



 8314 ð 349



D 0 .0138 kmol/m^3