Question

If the surface tension of a liquid is T, the gain in surface energy for an increase in liquid surface by A is

(A) $A{T^{ - 1}}$
(B) $AT$
(C) ${A^2}T$
(D) ${A^2}{T^2}$

Answer 1

Hint: A liquid's property called surface tension is common. The liquid's molecules all simultaneously sense force coming from all directions. Therefore, the net force on such molecules will be zero. The molecules on the liquid surface will only be subject to force from below because there are no molecules above them. Therefore, they have some surface energy.

Formula used:
$W=T\times \Delta A$
W is the work done, T is the surface tension and $\Delta A$ is the change in area

Complete answer:
Now from the question, we know that;
Surface tension of the liquid is T.
Change in surface area that is here increase in surface area of liquid is A.
We need to find out the gain in the surface energy.

In order to find out surface energy, first we need to know what is surface tension and surface energy of a liquid.

We know that surface tension in case of a liquid is the attractive force of the molecules present at the surface of a liquid towards each other and surface energy in the case of a liquid is the equivalent attractive force present between the molecules at the surface of the liquid.

Now we know,
Surface energy = surface tension*change in area
From the question, put the values here;
$surface\,energy = T \times A$
Hence the correct answer is Option B.

Note: We should be aware that the force that the molecules under the surface of the liquid exert on the molecules on the liquid's surface is what causes the property of surface tension to form. The liquid's molecules constantly have a propensity to pull the liquid's surface molecules into the bulk of the liquid. As a result, the molecules have a tendency to contract and occupy the smallest surface area. This surface tension force, which functions as a sort of cohesive force, is only felt while facing inward.