Question

Work done to blow a bubble of volume V is W. The work done in blowing a bubble of volume 2V will be ______.

Options

• (2)^1/3 W

• 2 W

• (4)^1/3 W

• 4 W

Answer 1

Work done to blow a bubble of volume V is W. The work done in blowing a bubble of volume 2V will be (4)^1/3 W.

Explanation:

From the definition of surface tension (T), the surface tension of a liquid is equal to the work (W) required to increase the surface area (A) of the liquid film by unity at constant temperature.

∴ W = T × ΔA

Since, surface area of a sphere is 4πR² and there are two free surfaces, we have

W = T × 8πR²        ...(i)

and volume of sphere = `4/3pi"R"^3`

i.e, V = `4/3pi"R"^3`

⇒ R = `((3"V")/(4pi))^(1//3)`            ...(ii)

From eqs. (i) and (ii) we get,

⇒ W ∝ V^2/3

W = T × 8π × `((3"V")/(4pi))^(2//3)`

∴ W₁ ∝ `"V"_1^(2//3)` and W₂ ∝ `"V"_2^(2//3)`

∴ `"W"_2/"W"_1=((2"V"_1)/"V"_1)^(2//3)`

⇒ W₂ = 2^2/3  W₁ = 4^1/3W