Chapter 22, Problem 22.1E

Using the explanation of unbalanced forces as the source of surface tension, justify why it requires energy to increase the surface area of a liquid. Is there any circumstance in which energy is given off when increasing a liquid’s surface area?

Interpretation Introduction

Interpretation:

The reason as to why unbalanced forces require energy to increase the surface area of a liquid is to be stated. If there is any circumstance in which energy is given off on increasing the surface area of a liquid is to be predicted.

Concept Introduction:

The atoms or molecules at the surface of the liquid are considered as a film. The atoms or molecules in bulk imply a force on the atoms or molecules at the surface of the liquid and tends to minimize the surface area of the liquid. This phenomenon is known as the surface tension of the liquid.

Answer to Problem 22.1E

If amount of force is $F$ and increase in surface is $dx$, then amount of work required to increase the surface area is shown below.

$dw=+F\cdot dx$

The $(+)$ sign indicates that work is done on the liquid. Work is a form of energy. Therefore energy must be applied to increase the surface area of a liquid.

Explanation of Solution

Different unbalanced forces act at the surface, so to increase the surface area of liquid, some work will be done against these unbalanced forces. If the amount of force is $F$ and increase in the surface is $dx$, then the amount of work required to increase surface area is shown below.

$dw=+F\cdot dx$

The $(+)$ sign indicates that work is done on the liquid. Work is a form of energy. Therefore, energy must be applied to increase the surface area of a liquid.

There are some situations in which energy is released by increasing the surface area. This occurs when the attraction between the interfaces is more than the attraction between molecules. This will cause a negative surface tension. An example of negative surface tension is capillary action.

Conclusion

If amount of force is $F$ and increase in surface is $dx$, then amount of work need to increase surface area is shown below.

$dw=+F•dx$

The $(+)$ sign indicates that work is done on the liquid. Work is a form of energy. Therefore energy must be applied to increase the surface area of a liquid.