Basic Chemical Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 34

TABLE 2.3
Surface Tensions of Some Common Substances
Compound Temperature (K) σ (mN/m)

Metals

Na 403 198

Ag 1373 878.5

Hg 298 485.5

Inorganic salts

NaCl 1346 115

NaNO 3 581 116

Gases

H 2 20 2.01

O 2 77 16.5

CH 4 110 13.7

Liquids
H 2 O 298 72.13
CHCl 3 298 26.67
CCl 4 298 26.43
C 6 H 6 293 28.88
CH 3 OH 293 22.50
C 8 H 17 OH 293 27.50
C 6 H 14 293 18.40
Source: Adamson,A.1990. PhysicalChemistryofSurfaces ,4thed.NewYork,
NY: John Wiley & Sons, Inc.

order to maintain the curved interface, a finite pressure difference ought to exist
between the inside, P i , and outside, P o , of the bubble. The work necessary to move
a volume d V of water from the bulk to the air bubble is given by (P i − P o ) d V . This

requires an extension of the surface area of the bubble by d A σ and the work done will
be

r 2 d r and d A σ = σ d A s . For a spherical bubble, d V = 4 π 8 π r d r . Therefore,

2 r .

Δ P = (2.62)

This is called the Young-Laplace equation. If we consider any curved interface that
can be generally described by its two main radii of curvatures, R 1 and R 2 , then the
Young-Laplace equation can be generalized as (Adamson, 1990;Adamson and Gast,
1997)

1
R 1 +

.

1
R 2

Δ P = σ (2.63)

The above equation is a fundamental equation of the capillary phenomenon . For a
plane surface, its two radii of curvature are infinite and hence P is zero. Capillarity

explains the rise of liquids in small capillaries, capillary forces in soil pore spaces,

Δ