Question

As soap bubble if radius r is surrounded by another soap bubble of radius 2r

Answer 1

Answer:

Explanation:A soap bubble of radius R is surrounded by another bubble of radius 2R. Take surface tension S. What will

be the pressure inside the smaller bubble in excess of atmospheric pressure?

Solution: According to the Laplace equation, excess pressure, created with surface tension of the

spherical surface of the liquid is equal to

R

S

p

2

  . In case of soap bubbles, the excess pressure of air

inside them is doubled due to the presence of two interfaces, one inside and one outside:

R

S

pb

4

  .

Excess pressure of the air inside the bigger bubble will be:

R

S

R

S

pB

2

2

4

   ;

Excess pressure of the air inside the smaller bubble will be: ;

4

R

S

p S  .

Air pressure difference between the smaller bubble and the atmosphere will be equal to the sum of

excess pressures inside the bigger and the smaller bubbles:

R

S

R

S

R

S

p p p B S

2 4 6

        .

Answer:

R

6S