Dep. Chem. Eng. – Heat and Mass Transfer I – Spring 2010

Assignment 1 Due: Monday May 31st at 4:00 p.m.

1. A gas mixture at a total pressure of 1.5 x 105 Pa and 295 K contains 20% H2, 40% O2,

and 40% H2O by volume. The absolute velocities of each species are -10 m/s, -2 m/s and

12 m/s, respectively, all in the direction of the z-axis. (10%)

a) Calculate the mass average velocity and the molar average velocity for the mixture.

b) Determine the four fluxes: jO2,z, nO2,z, JO2,z, NO2,z

∂ρ A

DwA

− rA = 0 , prove that ρ

+ ∇. j A − rA = 0 , where D stands

∂t

Dt

for substantial derivative (total derivative). (20%)

→ 2. Knowing that ∇. n A +

→ → n A = − DAB∇ρ A + wA n Hint:

→ ∇.ρ v + ∂ρ

=0

∂t 3. A 0.15-m-long, 0.015-m-diameter test tube containing ethanol is left open in the

laboratory. The level of ethanol is initially 0.1 m below the top. The temperature in the

laboratory is 26°C and the atmospheric pressure is 0.987 atm. The vapour pressure of

ethanol is 0.08 atm. If the concentration of ethanol in the air outside the test tube is

negligible and the concentration of ethanol near the liquid surface can be calculated using

Dalton’s law, determine:

(25%)

a) An expression for the concentration profile of ethanol in air inside the test tube if the

liquid level is held constant.

b) An expression for the instantaneous molar flux of ethanol.

c) The time required for the level of ethanol to decrease by 0.005 m if the evaporation

rate does not change with time. Remember that the decrease in ethanol level will be equal

to its rate of transfer to the gas phase:

dz

N A interface = C A,liq v A = C A,liq

dt

3

Data: density of ethanol: 784 kg/m .

Answer to (c) = 52 h

4. A 0.20-m-long test tube was used to study the diffusion process in which liquid A

diffuses into gas B. In one study the level of liquid A was initially 0.1 m below the top of

the tube. The temperature was 25°C and the total pressure was maintained at 1 atm. The

molar flux of component A at the top of the test tube was found to be 1.6x10-3

kgmol/m2.h. Find the diffusion coefficient for A into gas B. Assume that gas B is

insoluble in liquid A. The partial pressure of A at the surface of the liquid was 0.06 atm.

Answer = 0.063 m2/h

(20%)

5. Gas A diffuses through two immiscible liquids contained in a capillary tube as shown

below. The concentration of A at the bottom of the capillary tube is maintained at a

constant value. The partial pressure of A in the gas is 0.05 atm. The equilibrium

relationships for A in the two liquids are:

(25%) 1 Dep. Chem. Eng. – Heat and Mass Transfer I – Spring 2010

Assignment 1 Due: Monday May 31st at 4:00 p.m.

CA,I = 200 PA

CA,I = 2 CA,II

where PA has units of atm and CA has units of kgmol/m3. The concentration of A at Z2 is

3.0 kgmol/m3. The diffusivities of A in liquids I and II are 1.5 x 10-9 m2/s and 7.5 x 10-9

m2/s, respectively. The thickness of the liquid I layer (Z0 – Z1) is 0.02 m and of the liquid

II layer (Z1 – Z2) is 0.05 m. Assume that convective effects at the bottom of the capillary

tube are negligible and that liquid I has a very low vapour pressure. Calculate the molar

flux of A dissolving into liquid II and plot the concentration of A in liquids I and II as a

function of Z.

Answer = 1.5 x 10-7 kgmol/m2.s

Gas A

Liquid I Z0

Z1 Liquid II

Z2 2