Calculate the work done in increasing the radius of a soap bubble in air from 2 cm to 3 cm. The surface tension of the soap solution is 27 dyn/cm.

Explanation

Data ` r_(1) = 2cm., r_(2) = 3 cm , ` T = 27 dyn /cm
Initial surface area of the soap bubble = ` 2 xx 4pir_(1)^(2)`
Final surface area of the soap bubble ` = 2 xx 4 pir_(2)^(2)`
Increase in surface area =` 2 xx 4pir_(2)^(2) - 2 xx 4pir_(1)^(2) = 8 pi (r_(2)^(2) - r_(1)^(2))`
The work done = surface tension` xx ` increasse in surface area
` T xx 8 pi (r_(2)^(2) - r_(1)^(2))`
` = 27 xx 8 xx 3.142 [ (3) ^(2) - (2)^(2)]`
` = 27 xx 8 xx 31.42 (9-4) = 3393` ergs