Question

Find the difference of air pressure between the inside and outside of a soap bubble 5mm in diameter, if the surface tension is 1.6N/m
A. 2560 \[N/{{m}^{2}}\]
B. 3720 \[N/{{m}^{2}}\]
C. 1208 \[N/{{m}^{2}}\]
D. 950 \[N/{{m}^{2}}\]

Answer 1

Hint: Surface tension is the tendency of liquid surfaces to shrink into the minimum surface area possible. Surface tension allows insects, usually denser than water, to float and slide on a water surface. We can solve this question by just substituting the given values in the formula given below:
\[{{P}_{i}}-{{P}_{o}}=\dfrac{4T}{R}\]
Where, T is the surface tension of the soap bubble and R is the radius of the soap bubble.

Complete step-by-step answer:
For a soap bubble, the surface tension creates an extra pressure inside the soap bubble so that it balances the forces and gets stable. Now consider a soap bubble of radius R and surface tension T. Due to surface tension, the molecules on the surface film experience the net force in the inward direction normal to the surface of the film of the soap bubble.
Let \[{{P}_{i}}\] be the pressure inside the liquid drop and \[{{P}_{o}}\] be the pressure outside the soap bubble. Therefore, excess pressure inside the soap bubble is
\[p={{P}_{i}}-P\]
And this excess pressure inside a soap bubble is given by the expression
\[{{P}_{i}}-{{P}_{o}}=\dfrac{4T}{R}=\rho \]
Now, substituting the given values in the formula we get,
\[\rho =\dfrac{4T}{R}=\dfrac{4\times 1.6}{2.5\times {{10}^{-3}}}\]
\[=2560N/{{m}^{2}}\]
Hence, the correct option is option A.

Note: Surface tension is the tendency of liquid surfaces to shrink itself into the minimum surface area possible and this happens because at liquid–air interfaces the surface tension results from the greater attraction of liquid molecules to each other due to the cohesive forces than to the molecules in the air which exert adhesive forces.