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

Question

A soap bubble of radius r is blown up to form a bubble of radius 2r under isothermal conditions. If s is the surface tension of soap solution, the energy spent in doing so is (A) 6 π σ r2  (B) 3 π σ r2  (C) 24 π σ r2  (D) 12 π σ r2

Tardigrade Admin · Accepted Answer

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

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

$6 πσ r^{2}$

$3 πσ r^{2}$

$24 πσ r^{2}$

$12 πσ r^{2}$

$9 πσ r^{2}$

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 s is the surface tension of soap solution, the energy spent in doing so is

6πσr2

3πσr2

24πσr2

12πσr2

9πσr2

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