山东大学：《物理化学》课程教学资源（讲义资料）8.2 surface phenomenon of liquid-for students

88.2 Surface phenomenon of liquid Out-class reading Levine p. 387-390 13.2 Curved interfaces

§8.2 Surface phenomenon of liquid Out-class reading: Levine p. 387-390 13.2 Curved interfaces

88.2 Surface phenomenon of liquid 8.2.2 Curved surface and additional pressure l Curved liquid surface drop Convex surface Concave surfa In graduated cylinder

8.2.2 Curved surface and additional pressure drop 1. Curved liquid surface In graduated cylinder Convex surface Concave surface §8.2 Surface phenomenon of liquid

88.2 Surface phenomenon of liquid 8.2.2 Curved surface and additional pressure Convex surface Concave surface pex Pe ex pin=pex + Ap Pin=pax+△p Ap additional pressure For convex surface: Ap>0 For concave surface: Ap <0

p additional pressure Convex surface Concave surface For convex surface: p>0 For concave surface: p < 0 p p p in ex = +  pex 8.2.2 Curved surface and additional pressure §8.2 Surface phenomenon of liquid

88.2 Surface phenomenon of liquid 8.2.2 Curved surface and additional pressure Pm=P+△n(4p+c)ld=odA A=4r ex Ap= o8Ttrdr 2o 20 To increase the volume(dn of liquid at p Ap Laplace equation Ap+ dp

( )   p dp dV dA + = pex p p p in ex = +Δ To increase the volume (dV) of liquid at pex = p + dp dA p dV   = 3 3 4 V = r 2 A = 4r 2 p r   = 2 8 2 4 rdr p r dr r      = = Laplace equation pin 8.2.2 Curved surface and additional pressure §8.2 Surface phenomenon of liquid

88.2 Surface phenomenon of liquid 8.2.2 Curved surface and additional pressure For curved surface: 20 Ap p- For convex surface, r>0, Ap>0, point to Laplace-Young equation the interior of liquid; ris the radius of curvature For concave surface, 0, Ap <0, point to the gaseous phase; For plane e surface, r-)00, 4→0,Pax=Pin

1 2 1 1 p r r     = +     For curved surface: Laplace-Young equation r is the radius of curvature. For convex surface, r > 0, p > 0, point to the interior of liquid; For concave surface, r<0, p < 0, point to the gaseous phase; For plane surface, r →, p → 0, pex = pin, 2 p r   = 8.2.2 Curved surface and additional pressure §8.2 Surface phenomenon of liquid

88.2 Surface phenomenon of liquid 8.2.2 Curved surface and additional pressure For bubble 昵图网 wuu.nipic. com 40 P

For bubble 8.2.2 Curved surface and additional pressure §8.2 Surface phenomenon of liquid 4 p r   =

88.2 Surface phenomenon of liquid 8.2.3 Vapor pressure under curved surface 4=H,-H=「m中=Vm2 For liquid with plane surface p=1°+ RTIn p For liquid in droplet: 1=p°+R7lnp l=RTInPr M20 2Me The droplets gradually disappear and the n Kelvin equation water level in the beaker increases RTor For droplet or bubble

Δ   = − = = r m m V dp V pΔ  *   = + RT p ln For liquid with plane surface: For liquid in droplet: ln   r r = + RT p * 2 Δ ln Δ r m p M RT V p p r    = = = * 2 ln r p M p RT r   = Kelvin equation For droplet or bubble The droplets gradually disappear and the water level in the beaker increases. 8.2.3 Vapor pressure under curved surface §8.2 Surface phenomenon of liquid

88.2 Surface phenomenon of liquid 8.2.3 Vapor pressure under curved surface 2Ma r/ m 10-6 107 108 109 n P RTpr[p /P1.001 1.011 111 I 295 3.0 The change in vapor pressure is not 2.5 large enough to be of any concern in 0 the case of macroscopic systems, such 1.5 as d>10-7m, or 0.1 um 10 0.5 0.01.0×10820×10830×10840×1085.0×1080×108 r/m

* 2 ln r p M p RT r   = r / m 10-6 10-7 10-8 10-9 pr / p * 1.001 1.011 1.111 2.95 The change in vapor pressure is not large enough to be of any concern in the case of macroscopic systems, such as d > 10-7 m, or 0.1 m. 8.2.3 Vapor pressure under curved surface §8.2 Surface phenomenon of liquid

88.2 Surface phenomenon of liquid 8.2.3 Vapor pressure under curved surface If a vapor is cooled or compressed to a pressure equal to the vapor pressure of the bulk liquid condensation should occur

8.2.3 Vapor pressure under curved surface §8.2 Surface phenomenon of liquid If a vapor is cooled or compressed to a pressure equal to the vapor pressure of the bulk liquid, condensation should occur

88.2 Surface phenomenon of liquid 8.2.3 Vapor pressure under curved surface (1)supersaturated vapor/supercooling The difficulty is that the first few molecules condensing can only form a minute drop and the vapor pressure of such a drop will be much higher than the regular vapor pressure

(1) supersaturated vapor / supercooling The difficulty is that the first few molecules condensing can only form a minute drop and the vapor pressure of such a drop will be much higher than the regular vapor pressure. p = p * pr = 2.95p * 8.2.3 Vapor pressure under curved surface §8.2 Surface phenomenon of liquid