Surface Areas And Volumes

Step 1: Recall the formula for the surface area of gas bubbles.
The surface area of a single spherical gas bubble is given by the formula: Where is the radius of the gas bubble.
Step 2: Convert the diameter into radius.
The average diameter of air bubbles is given as , so the radius will be: Step 3: Calculate the surface area of a single bubble.
Substituting into the formula for surface area: Step 4: Calculate the total surface area of bubbles per liter of reactor.
The gas hold-up is 10%, meaning 10% of the reactor volume is occupied by gas bubbles. For a reactor with volume (in this case 1 liter = 1000 cm ), the total volume of gas bubbles is . The total number of bubbles in the reactor, assuming they are spherical with volume , is: The number of bubbles in the reactor is: Step 5: Calculate the total surface area of the bubbles. The total surface area of all the bubbles in the reactor is: