Concise Physical Chemistry

c11 JWBS043-Rogers September 13, 2010 11:26 Printer Name: Yet to Come

166 LIQUIDS AND SOLIDS

FIGURE 11.1 Intermolecular attractive forces acting upon molecules at an air–water

interface.

variable force per unit lengthγ≡f/ltimes the infinitesimal increase in areadσ:

dw=

(

f

l

)

dσ=γdσ

The intensive variable force per unit lengthγ=f/lin the two-dimensional model

replaces the intensive variable pressure that is force per unit area of the piston face

p=f/Ain the three-dimensional model of a piston and cylinder. Please do not

confuse the area of the piston faceAwith the area of the liquid filmσ.

From the physics of vibration of stretched strings, we have the force per unit length

f/ldefined as atension. Becausedσis an infinitesimal increment in thesurfacearea

of the membrane, the intensive variableγ=f/lis called thesurface tension.

Imagine a minute device such as that in Fig. 11.3 immersed in a soap solution

and drawn up so that a film of the liquid occupies the areaσthat can be expanded

an amountdσby an upward forcefon an edge of lengthl. Because the tension

γarises from the surfaces on either side of the liquid membrane drawn up into the

framework, the work of expanding the bimembrane (a memebrane with two sides

or surfaces) is twice the work for each surface,dw= 2 γdσ. The expansion of the

surface isdσ=ldh, wheredhis the increase in height of the movable edge of length

l. In general, work is a force times a displacement, sodw= 2 γdσ= 2 γldh.

σ f/l

dσ

l

FIGURE 11.2 Stretching a two-dimensional membrane by moving an edge of lengthl.A

real liquid would have two films, one facing you on the front surface of the page and one on

the back surface.