The interfacial area per unit volume of dispersion, in a gas-liquid contactor, for fractional hold up of gas = 0.1 and gas bubble diameter = 0.5 mm is given by (in m²/m³)

To calculate the interfacial area per unit volume (denoted as
𝑎
a, in m²/m³) for a gas-liquid dispersion, we use the formula:

𝑎
=
6
⋅
𝜀
𝑔
𝑑
𝑏
a=
d
b
​

6⋅ε
g
​

​

Where:

𝜀
𝑔
ε
g
​
= gas holdup (fractional)

𝑑
𝑏
d
b
​
= bubble diameter (in meters)

Given:
𝜀
𝑔
=
0.1
ε
g
​
=0.1

𝑑
𝑏
=
0.5
 
mm
=
0.0005
 
m
d
b
​
=0.5mm=0.0005m

Substituting into the formula:
𝑎
=
6
×
0.1
0.0005
=
0.6
0.0005
=
1200
 
m
2
/
m
3
a=
0.0005
6×0.1
​
=
0.0005
0.6
​
=1200m
2
/m
3

✅ Correct answer:
B. 1200

The interfacial area per unit volume of dispersion (a) can be calculated using the following formula:

a = 6 × ε / d

where:
ε = fractional hold-up of gas = 0.1
d = gas bubble diameter = 0.5 mm = 0.0005 m

Substituting the values:

a = 6 × 0.1 / 0.0005
= 6 × 200
= 1200 m²/m³

So, the interfacial area per unit volume of dispersion is 1200 m²/m³.

Formula for interfacial Area per unit volume = 6 (1-e)/Dp
a = 1200
Option B is Right

Answer is B.