Correct Answer - Option 1 : A = 2B
Explanation:
- The surface tension of water provides the necessary wall tension for the formation of bubbles with water. The tendency to minimize that wall tension pulls the bubbles into spherical shapes.
- The pressure difference between the inside and outside of a bubble depends upon the surface tension and the radius of the bubble.
- The relationship can be obtained by visualizing the bubble as two hemispheres and noting that the internal pressure which tends to push the hemispheres apart is counteracted by the surface tension acting around the circumference of the circle.
- For a bubble with two surfaces providing tension, the pressure relationship is:
\(P_i - P_o = \frac{4T}{r}\)
Bubble Pressure: The net upward force on the top hemisphere of the bubble is just the pressure difference times the area of the equatorial circle:
\(F_{upward} = (P_i - P_o)\pi r^{2}\)
- The force of the surface tension downward on the entire circumference of the circle is twice the surface tension times the circumference since two surfaces contribute to the force.
\(F_{downward}= 2T(2 \pi r)\)
This gives
\(P_i - P_o = \frac{4T}{r} \) for a bubble
\(P_i - P_o = \frac{2T}{r} \) for a droplet that has only one surface.
Surface tension on a liquid droplet (Spherical droplet of water):
Pressure intensity inside the droplet:
\(p = \frac{{4σ }}{d}\)
In the question surface tension for the liquid droplet = A
Replacing σ with A in the above equation we get
\(A = \frac{{pd }}{4}\)
Surface tension on a hollow bubble (Soap bubble): w
Pressure intensity inside the bubble:
\(p = \frac{{8σ }}{d}\)
In the question, the surface tension in a hollow bubble = B
Replacing σ with b ion the above equation we get
\(B = \frac{{pd }}{8}\)
Thus, A = 2B
