Question

Two spherical soap bubbles of different radii coalesce. If V is the consequent change in volume of the contained air, and S the change in the total surface area, then show that 3PV + 4ST = 0, where T is surface tension of the soap solution.       

Solution

Correct option is

 

Let R1 and R2 be the radii of the bubbles, and R the radius of the bigger bubble. Let P be the atmospheric pressure. If p1 and p2 be the pressures inside the bubbles before coalescing and p the pressure inside the bigger bubble formed. Then 

             

If V1V2, and V be the corresponding volumes of the bubbles, then

. If temperature is constant, then by Boyle’s law, we have  

             

       

  

.

SIMILAR QUESTIONS

Q1

The fresh water behind a reservoir dam is 15 m deep. A horizontal pipe 4.0 cm in diameter passes through the dam 6.0 m below the water surface as shown in figure. A plug secures the pipe opening. The plug is removed. What volume of water flows out of the pipe in 3.0- hour?     

                                                          

Q2

A soap film is on a rectangular wire ring of size . If the size of the film is changed to , then calculate the work done in this process. The surface tension of soap film is 

Q3

The surface tension of a soap solution is 0.03 N/m. How much work is required to form a bubble of 1.0 cm radius from this solution? 

Q4

A mercury drop of radius 1.0 mm breaks up into 64 droplets of equal volumes. Calculate the work done in this process. (Surface tension is mercury is 0.465 N/m)  

Q5

 

A big drop is formed by coalesing 1000 small droplets of water. What will be the change in surface energy? 

What will be the ratio between the total surface energy of the droplets and the surface energy of the big drop?

Q6

 joule work is being done in breaking a big drop of water of radius R into 1000 small drops of equal size. Find out the surface tension of water.

Q7

A drop of mercury has a radius of 3.00 mm at room temperature. The surface tension of mercury at that temperature is 0.465 Nm–1. Find excess pressure inside the drop and the total pressure inside the drop. The atmospheric pressure is .

Q8

What is the excess pressure in a soap bubble of radius 5.00 mm at 20oC? The surface tension of soap solution at 20oC is .

Q9

 

If an air bubble of same radius be formed at a depth of 40.0 cm in a soap solution (relative density 1.20), then what will be the pressure inside the air bubble?

Q10

The limbs of a manometer consist of uniform capillary tubes of radii . Find out the pressure difference if the level of the liquid (density 103 kg/m3, surface tension ) in the narrower tube stands 0.2 m above that in the broader tube.