Question

A soap bubble of diameter $7$ cm, its diameter is increased to $14$ cm. If change in its surface energy is $(15000 - x)\,\mu$J, find $x$. (Given surface tension = $0.04$ N/m)

• A. $208$
• B. $216$
• C. $432$
• D. $512$

Hint:

For soap bubbles, always remember that there are two surfaces contributing to surface energy.

Answer 1

The Correct Option is B

To find the change in surface energy of a soap bubble and determine the value of x, we use the concept of surface tension and change in surface area.

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Given:

Initial diameter, d₁ = 7 cm
Final diameter, d₂ = 14 cm
Surface tension, T = 0.04 N/m

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Step 1: Write the formula for surface energy

Change in surface energy,
ΔE = T × ΔA

A soap bubble has two surfaces (inner and outer), hence:

ΔA = 2 × (4πR₂² − 4πR₁²)

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Step 2: Calculate radii

R₁ = 7/2 = 3.5 cm = 0.035 m
R₂ = 14/2 = 7 cm = 0.07 m

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Step 3: Calculate change in surface area

ΔA = 2 × 4π (0.07² − 0.035²)

ΔA = 8π (0.0049 − 0.001225)

ΔA = 8π × 0.003675

ΔA ≈ 0.0922 m²

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Step 4: Calculate change in surface energy

ΔE = T × ΔA

ΔE = 0.04 × 0.0922

ΔE ≈ 0.003688 J

ΔE = 3688 μJ

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Step 5: Determine the value of x

Given relation:
15000 − x = 3688

x = 15000 − 3688

x = 216

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Final Answer:

The correct value of x is
x = 216