Question

Two spherical soap bubbles of radii r₁ and r₂ in vacuum coalesce under isothermal conditions. The resulting bubble has a radius R such that ____________.

पर्याय

• R = (r₁ + r₂)/2

• R = [r₁r₂/(r₁ + r₂)]

• `"R" = sqrt("r"_1^2 + "r"_2^2)`

• R = r₁ + r₂

Answer 1

Two spherical soap bubbles of radii r₁ and r₂ in vacuum coalesce under isothermal conditions. The resulting bubble has a radius R such that `underlinebb("R" = sqrt("r"_1^2 + "r"_2^2))`.

Explanation:

Because the bubbles coalesce in a vacuum, there is no temperature change. As a result, the surface energy remains unchanged. This means that the total surface area is unaffected.

Hence `4pi"r"_1^2 + 4pi"r"_2^2 = 4pi"rR"^2`

`"or R" = ["r"_1^2 + "r"_2^2]^(1/2)`