Page:Elementary Text-book of Physics (Anthony, 1897).djvu/108

 the length of the rod, or the force applied per unit of length, measures the surface tension.

81. Energy and Surface Tension.—If the shape of the liquid mass be changed in such a way that its surface increases, work must be done upon those molecules which pass from the interior into the surface. This may either be viewed as work done upon each molecule as it is forced out of the interior mass, where the forces upon it are in equilibrium, into the surface layer, in which it is acted on by a force normal to the surface and in which therefore a movement along that normal involves the doing of work; or it may be looked on as work done against the tension acting in the surface. We call the potential energy gained when the surface increases by one unit the surface energy per unit of surface; we will show that it is numerically eqiial to the surface tension per unit of length.

Suppose a thin film of liquid to be stretched on a frame $$ABCD$$ (Fig. 29), of which the part $$BCD$$ is solid and fixed, and the part $$a$$ is a light rod, free to slide along $$C$$ and $$D$$. This film tends, as we have said, to diminish its free surface. As it contracts, it draws $$A$$ towards $$B$$. If the length of $$A$$ be $$a$$, and $$A$$ be drawn towards $$B$$ over $$b$$ units, and if $$E$$ represent the surface energy per unit of surface, the energy lost, or the work done, is expressed by $$Eab$$. If we consider the tension acting normal to $$A$$, the value of which is $$T$$ for every unit of length, we have again for the work done during the movement of $$A$$, $$Tab$$. From these expressions we obtain at once