A soap bubble of radius r is blown up to form a bubble of radius 2r under isothermal conditions. If σ is the surface tension of the soap solution, the energy spent in the process is

Question

A soap bubble of radius r is blown up to form a bubble of radius 2r under isothermal conditions. If σ is the surface tension of the soap solution, the energy spent in the process is (A) 6π σ r2 (B) 24π σ r2 (C) 12π σ r2 (D) 9π σ r2

Tardigrade Admin · Accepted Answer

Energy spent = Work done = TΔ A Here, A is total surface area ∴ A=8π r2 for soap bubble Hence, energy spent =σ [8 π (2 r)2 - 8 π r2] =σ (32 π r2 - 8 π r2) =24π σ r2

Q. A soap bubble of radius $r$ is blown up to form a bubble of radius $2 r$ under isothermal conditions. If $σ$ is the surface tension of the soap solution, the energy spent in the process is

$6 πσ r^{2}$

$24 πσ r^{2}$

$12 πσ r^{2}$

$9 πσ r^{2}$

$18 πσ r^{2}$

Energy spent $=$ Work done $=$ $T Δ A$
Here, $A$ is total surface area
$∴ A = 8 π r^{2}$ for soap bubble
Hence, energy spent $= σ [8 π (2 r)^{2} - 8 π r^{2}]$
$= σ (32 π r^{2} - 8 π r^{2})$
$= 24 πσ r^{2}$

Q. A soap bubble of radius r is blown up to form a bubble of radius 2r under isothermal conditions. If σ is the surface tension of the soap solution, the energy spent in the process is

6πσr2

24πσr2

12πσr2

9πσr2

18πσr2

Energy spent = Work done = TΔA Here, A is total surface area ∴A=8πr2 for soap bubble Hence, energy spent =σ[8π(2r)2−8πr2] =σ(32πr2−8πr2) =24πσr2