Question

The radius of a soap bubble is r. The surface tension of soap solution is S. Keeping temperature constant, the radius of the soap bubble is doubled, the energy necessary for this will be :

a. 24 πr²S
b. 8 πr²S
c. 12 πr²S
d. 16 πr²S

Answer 1

The energy required to double the radius of a soap bubble, considering its surface tension, corresponds to option a, which is 24πr²S.option a is correct answer.

Step-by-step explanation:

The energy required to double the radius of a soap bubble, keeping temperature constant, can be found by considering the work done to expand the surface area of the bubble due to the surface tension of the soapy solution. The work done is equal to the force times the distance over which the force is applied, which in this case is related to the change in surface area of the bubble.

For a soap bubble, the initial surface area with radius r is 4πr² and it is doubled when the radius is doubled (to 2r). Hence, the new surface area becomes 4π(2r)² = 16πr². The change in surface area is 16πr² - 4πr² = 12πr². Since the bubble has an inside and an outside surface, the total change in surface area is 2 × 12πr² = 24πr².

The energy required to increase the area is the change in area multiplied by the surface tension, S. Therefore, the energy necessary for doubling the radius of the bubble is 24πr²S, which corresponds to option a.