Question

If be the work to be done to form a bubble of volume V from a given solution. The work required to be done to form a bubble of volume 2 V is

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

Answer 2

Here, volume of bubble,

$\mathrm { V } = \frac { 4 } { 3 } \pi \mathrm { R } ^ { 3 }$ Or

Work done, $\mathrm { W } = \mathrm { S } \times 8 \pi \mathrm { R } ^ { 2 } = \mathrm { S } \times 8 \pi \left( \frac { 3 \mathrm {~V} } { 4 \pi } \right) ^ { 2 / 3 }$

Or

$\therefore \frac { \mathrm { W } _ { 2 } } { \mathrm {~W} _ { 1 } } = \left( \frac { \mathrm { V } _ { 2 } } { \mathrm {~V} _ { 1 } } \right) ^ { 2 / 3 } = \left( \frac { 2 \mathrm {~V} } { \mathrm {~V} } \right) ^ { 2 / 3 }$

$= 2 ^ { 2 / 3 }$

$\therefore \mathrm { W } _ { 2 } = 4 ^ { 1 / 3 } \mathrm {~W} _ { 1 }$