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Question: A rectangular film of liquid is extended from (4cm×2cm) to (5cm×4cm). If the work done is \(3 \times...

A rectangular film of liquid is extended from (4cm×2cm) to (5cm×4cm). If the work done is 3×10−4J3 \times {10^{ - 4}}J, the value of the surface tension of the liquid is
A. 0.250 Nm−10.250{\text{ }}N{m^{ - 1}}
B. 0.125 Nm−10.125{\text{ }}N{m^{ - 1}}
C. 0.2 Nm−10.2{\text{ }}N{m^{ - 1}}
D. 8.0 Nm−18.0{\text{ }}N{m^{ - 1}}

Explanation

Solution

Generally the property of liquid is surface tension. All the molecules inside the liquid experience force from all the 360 degrees direction. Hence net force will be zero on those molecules. The molecules which are on the liquid surface will be experiencing force only from below molecules as there are no molecules above them. So they have some surface energy.
Formula used:
S=2TΔAS = 2T\Delta A
ΔA=Af−Ai\Delta A = {A_f} - {A_i}

Complete answer:
When a liquid film is extended, the area of that film gets increased and then the surface energy of that film gets increased. Energy cannot be created nor destroyed. Hence the extra energy generated must be coming from somewhere. The work we do will be converted to energy and stored as that extra energy. Now change in the energy will give us the work done. Change in surface energy will be 2TΔA2T\Delta A. Where T is the surface tension and ΔA\Delta A is the change in surface area.

We have ΔA = (5×4) - (4×2) = 12cm2\Delta A{\text{ = (5}} \times {\text{4) - (4}} \times {\text{2) = 12c}}{{\text{m}}^2}
This change in energy will become equal to the work done. Where work done is 3×10−4joules3 \times {10^{ - 4}}joules
So work done will be equal to the change in the surface energy.
W=2TΔAW = 2T\Delta A
3×10−4joules=2T×12×10−4m23 \times {10^{ - 4}}joules = 2T \times 12 \times {10^{ - 4}}{m^2}
So 3×10−4joules=T×24×10−4m23 \times {10^{ - 4}}joules = T \times 24 \times {10^{ - 4}}{m^2}
T=324=0.125 Nm−1T = \dfrac{3}{{24}} = 0.125{\text{ }}N{m^{ - 1}}

So, the correct answer is “Option B”.

Note:
In the change in surface energy formula we have a multiplication factor of 2 because there will be two surface areas which will be in contact with the metal piston or the surface which is in contact with the film. So each film contains the same surface energy and since there are two films we will multiply with two. Every liquid tries to minimize its surface energy and hence water drops are spherical in shape as they have less surface area and hence less surface energy.