Question

The pressure of air in a soap bubble of 0.7cm diameter is 8 mm of water above the pressure outside. The surface tension of the soap solution is

• A. 100 dyne/cm
• B. 68.66 dyne/cm
• C. 137 dyne/cm
• D. 150 dyne/cm

Answer 1

The correct option is

D

Step 1: Given

Excess pressure=8 mm of water= 0.008 m of water.

Diameter of bubble=0.7 cm= 0.007 m

Radius(r)=0.007/2 m = 0.0035 m

Let Excess pressure = P

T is surface tension

The density of water(ρ) = 1000 $\frac{kg}{m^3}$

Step 2: Formula used

P = ρ*g*h

P = 4 $\frac{T}{r}$ (Surface tension)

Step 3: Finding surface tension

Excess pressure(P)= 8 mm of water = 1000*9.8*0.008 Pa = 78.4 Pa

P=4$\frac{T}{r}$

(78.4*0.0035)/4=T

T=0.0686 $\frac{N}{m}$

T= 68.66$\frac{dyne}{cm}$

Hence, the surface tension inside the bubble is 68.66 $\frac{dyne}{cm}$.