How much work is required to form a bubble of 2 cm radius from the soap solution having surface tension 0.07 N/m.
After going through the question, we observe some data as ,
initial radius = 0cm
final radius , r= 2cm = 0.02 m
dr = 2cm = 0.02 m
Surface Tension (T) = 0.07 N/m
The formula to calculate the work done to form a bubble is
Work = Surface Tension x Change in Surface Area
Initial Surface Area = 4πr²
Final Surface Area = 4π(r + dr)²
Change in Surface Area = Final Surface Area - Initial Surface Area
= 4π(r + dr)² - 4πr²
= 4π(r² + 2rdr + dr²) - 4πr² = 4πr² + 8πrdr + 4πdr² - 4πr²
= 8πrdr + 4πdr²
Since the change in radius (dr) is very small compared to the initial radius (r), we can neglect the dr² , hence 4πdr² is neglected
Change in Surface Area ≈ 8πrdr
Work = Surface Tension x Change in Surface Area = 0.07 x 8πrdr = 0.07 x 8 x 3.142 x 0.02 x 0.02 =
= 0.000224 x 3.142
= 7.038 x 10^-4 J
