To find the work done in increasing the size of a soap bubble, we need to understand that a soap bubble has two surfaces (inner and outer), and work is done against surface tension to increase the surface area.

Step 1: Formula for Work Done
The work done (W) to change the surface area of a bubble is given by: $W=T\times \mathrm{\Delta A}$ where T is the surface tension and ΔA is the change in total surface area.

Step 2: Change in Surface Area
For a soap bubble, the total surface area is twice that of a solid sphere (because of two surfaces). Initial radius, r₁ = 3 cm = 0.03 m, Final radius, r₂ = 5 cm = 0.05 m.
Initial total surface area, A₁ = 2 × 4πr₁² = 8πr₁²
Final total surface area, A₂ = 2 × 4πr₂² = 8πr₂²
So, change in area, ΔA = A₂ - A₁ = 8π(r₂² - r₁²)

Step 3: Substitute Values
Given T = 0.03 N/m
r₁ = 0.03 m, r₂ = 0.05 m
r₂² = (0.05)² = 0.0025 m²
r₁² = (0.03)² = 0.0009 m²
r₂² - r₁² = 0.0025 - 0.0009 = 0.0016 m²
ΔA = 8π × 0.0016 = 0.0128π m²

Step 4: Calculate Work Done
W = T × ΔA = 0.03 × 0.0128π = 0.000384π J
Since 1 mJ = 10⁻³ J, W = 0.000384π × 1000 mJ = 0.384π mJ ≈ 0.4π mJ

Final Answer: 0.4π mJ

Related Topics and Formulae

Surface Tension: It is the property of a liquid that allows it to resist an external force, due to cohesive forces between molecules. The work done to increase surface area is W = T × ΔA.

Soap Bubble: Has two surfaces, so total area is twice the area of a sphere. For a sphere of radius r, surface area is 4πr², so for bubble it is 8πr².

Units: Surface tension T in N/m, area in m², work in Joules (J).