Calculate the work done in blowing out a soap bubble of diameter 1.0cm .the surface tension of soap solution is 0.028N/m

To calculate the work done in blowing out a soap bubble, we need to consider the concept of surface tension and how it relates to the surface area of the bubble. The work done is essentially the energy required to increase the surface area of the bubble as it expands.

Understanding Surface Area and Surface Tension

A soap bubble has two surfaces: the outer surface and the inner surface. When you blow a bubble, you are increasing the surface area of both of these surfaces. The formula for the surface area (A) of a sphere is given by:

• A = 4πr²

Where r is the radius of the sphere. Given that the diameter of the bubble is 1.0 cm, we first need to convert this to meters to maintain consistency in our units:

• Diameter = 1.0 cm = 0.01 m
• Radius (r) = Diameter / 2 = 0.01 m / 2 = 0.005 m

Calculating the Total Surface Area

Now, let's calculate the total surface area of the bubble:

• Surface area of one surface (A) = 4π(0.005 m)²
• A ≈ 4π(0.000025 m²) ≈ 0.00031416 m²

Since the bubble has two surfaces, the total surface area (A_total) becomes:

• A_total = 2 × 0.00031416 m² ≈ 0.00062832 m²

Work Done Calculation

The work done (W) in blowing up the bubble can be calculated using the formula:

• W = Surface Tension (σ) × Change in Surface Area (ΔA)

In this case, the change in surface area is equal to the total surface area since we start from no bubble (A_initial = 0). Thus, ΔA = A_total.

Substituting the values:

• W = σ × A_total
• W = 0.028 N/m × 0.00062832 m²
• W ≈ 0.0000176 N·m = 0.0000176 Joules

Final Result

Therefore, the work done in blowing out a soap bubble of diameter 1.0 cm, with a surface tension of 0.028 N/m, is approximately:

• 0.0000176 Joules

This small amount of energy illustrates how relatively little work is needed to form such a delicate structure as a soap bubble, thanks to the properties of surface tension.