Question

A rectangular soap film is $5 \mathrm{~cm}$ long and $4 \mathrm{~cm}$ wide. If the work done in increasing its area $7 \mathrm{~cm} \times 5 \mathrm{~cm}$ is $0.06 \mathrm{~J},$ the surface tension of the soap solution is:
A) $0.2 \mathrm{~J} / \mathrm{m}^{2}$
B) $2 \mathrm{~J} / \mathrm{m}^{2}$
C) $20 \mathrm{~J} / \mathrm{m}^{2}$
D) $72 \mathrm{~J} / \mathrm{m}^{2}$

Answer 1

Hint: We know that every liquid has a tendency to shrink into the minimum required surface that is possible within the availability. This property of the liquids is known as surface tension of the liquid. The soap solution in the question shows this kind of property.

Complete step by step answer:
We know that to answer this question we have to find the work done by the tension. The expression to find the work done by the tension is given as:
$\mathrm{W}=\mathrm{T}(2 \Delta \mathrm{A})$
Now from the above expression, we know that we have to find the value of tension or T. Thus, we can write the expression as:
$\Rightarrow \mathrm{T}=\mathrm{d} \dfrac{\mathrm{W}}{2 \Delta \mathrm{A}}$
In the above expression we have to put the values to get the answer. Thus, the expression formed is given as:
$\Rightarrow \dfrac{0.06}{2(7 \times 5-5 \times 4) \times 10^{-4}}=20 \mathrm{Jm}^{-2}$
Hence, we can say that the tension of the soap solution is $20 \mathrm{~J} / \mathrm{m}^{2}$.

So, the correct option is Option C.

Additional Information:
Cohesive force is defined as the intermolecular force that is responsible for the bulk property that exists among the liquids. Because of this force the liquids always resist separation.

Note: We should know that the reason behind the production of the property of surface tension is the force that is exerted on the molecules that are present on the surface of the liquid, by the molecules that are present underneath. The molecules that are present in the liquid always have a tendency to bring the surface molecules of the liquid inside the bulk. Thus, the molecules tend to shrink and occupy the least possible surface area. This force of surface tension is experienced only towards the inward and is a kind of cohesive force.