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Chapter 7: Problem 996

The relation between surface tension T. Surface area \(\mathrm{A}\) and surface energy \(\mathrm{E}\) is given by. (A) \(\mathrm{T}=(\mathrm{E} / \mathrm{A})\) (B) \(\mathrm{T}=\mathrm{EA}\) (C) \(\mathrm{E}=(\mathrm{T} / \mathrm{A})\) (D) \(\mathrm{T}=(\mathrm{A} / \mathrm{E})\)

Short Answer

Expert verified
The correct relation between surface tension (T), surface area (A), and surface energy (E) is given by option (B): \(T=EA\).

Step by step solution

01

Recall the definition of surface tension

Surface tension is a property of liquid surfaces which makes them behave as if they are covered with a stretched elastic membrane. This tension arises due to an imbalance in the molecular cohesive forces at the surface. Surface energy is the extra energy that molecules at the surface possess due to the imbalance of force.
02

Relate surface tension to surface energy and surface area

The relation between surface tension, surface energy, and surface area can be established by considering a change in surface area. The work done to increase the surface area is equal to the increase in surface energy. Mathematically, this can be represented as: \[ dE = T dA \] This equation states that the differential work (\(dE\)) required to change the surface area by a small amount (\(dA\)) is equal to the product of the surface tension (T) and change in surface area (\(dA\)). Integrating both sides of the equation will give us the relation between surface energy, surface tension, and surface area: \[ E = T A \]
03

Identify the correct option

Now that we have derived the relationship between surface tension (T), surface area (A), and surface energy (E): \[ E = TA \] We can see that the correct relation corresponds to option (B): \(T=EA\).

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Most popular questions from this chapter

The variation of density of water with temperature is represented by the

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