226
5 Phase Equilibrium
h
h
␪
(a)
(b)
(c)
h
Figure 5.17 Capillary Rise or Depression of a Liquid in a Tube. (a) A liquid that wets
the solid surface. (b) A liquid that partially wets the solid surface. (c) Capillary depression
of mercury in a glass capillary.
E X A M P L E 5.11
Find the height to which water at 20 ◦ C will rise in a glass capillary tube of diameter 0.60 mm.
Solution
From Table A.10, γ 0.07275 J m −2 .
h
2γ
ρgr
2 (0.07275 J m −2 )
(1000 kg m −3 )(9.80 m s −2 )(0.30 × 10 −3 m)
0.049 m 4.9 cm
Exercise 5.14
Find the height to which the surface of water will rise in a glass tube with a diameter equal to
6.0 cm.
If the contact angle θ is not equal to zero, the surface tension force is exerted at an
angle of θ from the vertical. Its upward component is equal to 2πrγ cos(θ), and the
height to which the liquid rises is
h
2γ cos(θ)
ρgh
(5.5-9)
Mercury atoms are attracted so weakly to glass compared with their attractions for each
other that mercury forms a contact angle with glass nearly equal to 180 ◦ . The surface