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# Surface tension of liquids using capilary tube

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• 1. Experiment 1, page 1 Version of March 2, 2006Experiment 446.1SURFACE TENSION OF LIQUIDSTheory To create a surface requires work that changes the Gibbs energy of a thermodynamicsystem. dG = − SdT + VdP + γdA (1.1)where γ is the surface tension, the free energy per unit surface area. Since a surface alwaysinvolves two phases, the surface tension depends on the nature of the two substances betweenwhich the surface is formed. If surface segregation of material occurs in a solution, then thesurface tension of the solution may depend on concentration in complex ways. Like otherthermodynamic variables, surface tension depends on conditions such as the temperature. Eq.(1.1), for example, shows that the temperature derivative of γ is given by the following Maxwellequation: ⎛ ∂γ ⎞ ⎛ ∂S ⎞ ⎜ ⎟ = −⎜ ⎟ (1.2) ⎝ ∂T ⎠ P ⎝ ∂A ⎠ Twhere the derivative on the right is known as the surface entropy. One can evaluate the surfaceentropy by investigating the manner in which the surface tension varies with temperature. Reports of surface tension are often given for the situation in which the second phase isair or the vapor of the material. Thus, for example, at 20°C, the reported surface tension ofbenzene against air is 28.85 dyne/cm, whereas the reported surface tension of benzene against itsvapor is reported to be 28.89 dyne/cm. In Table 1.1 are data on the surface tension of wateragainst air. Surface tensions for liquids against liquids are called interfacial tensions. Suchinterfacial tensions can be very different from the surface tensions of liquids against air. Forexample, the interfacial tension of water against benzene is 35 dyne/cm at 20°C, whereas itsvalue against air is 73.05 dyne/cm, and that of benzene against air is 28.85 dyne/cm. Surface tension produces several observable phenomena. The rise of a liquid in acapillary is the result of surface tension. The spreading of a film of oil on water is anotherexample of the effect of surface tension, something first reported by Benjamin Franklin, althoughit probably was known in antiquity. Consider the simple situation depicted in Fig. 1.1, in which the end of a capillary tube ofradius, r, is immersed in a liquid. For sufficiently small capillaries, one observes a substantialrise of liquid to height, h, in the capillary, because of the force exerted on the liquid due tosurface tension. Equilibrium occurs when the force of gravity balances this force due to surfacetension. The balance point can be used as a means to measure the surface tension: γ (2πr ) = ρ h (πr 2 ) g (1.3)
• 2. Experiment 1, page 2 Version of March 2, 2006Table 1.1. Density and Surface Tension of Water Against Air at Various TemperaturesaTemperature Density γ Temperature Density γ (°C) (gm/cm3) (dyne/cm) (°C) (gm/cm3) (dyne/cm) 0 0.99987 75.6 30 0.99567 71.18 5 0.99999 74.9 40 0.99224 69.56 10 0.99973 74.22 50 0.98807 67.91 15 0.99913 73.49 60 0.98324 66.18 18 0.99862 73.05 70 0.97781 64.4 20 0.99823 72.75 80 0.97183 62.6 25 0.99707 71.97 100 0.95838 58.9a Source: R. C. Weast and M. J. Astle, Eds., CRC Handbook of Physics and Chemistry, 63rdEdition, CRC Press, Boca Raton, Florida, 1982. where r is the radius of the capillary, h Figure 1. 1. Schematic diagram showing is the capillary rise, ρ is the liquid liquid rise in a capillary of radius r. density, g is the acceleration due to gravity1, and γ is the surface tension of the liquid. Rearrangement gives a simple expression for the surface tension: 1 γ = ρ grh (1.4) 2 A careful look at the boundary shows that the surface is not perfectly flat. Instead it curves up (or sometimes down) at the wall to form a meniscus, as shown in the inset in Fig. 1.1. The material in this region also contributes to the force of gravity, so one often finds a correction to Eq. (1.4) to yield 1 r Figure 1.1. Capillary rise due to surface tension. γ ρ g r (h + ) = (1.5) 2 3 where the contact angle (the anglebetween the surface of the liquid and surface of the glass) has been assumed to be 0°.Procedure In this experiment you determine the surface tension of liquids against air by the methodof capillary rise. To get good results, you must pay attention to cleanliness and procedure. If the1 The standard acceleration due to gravity is defined by the International Committee on Weights and Measures to be980.665 cm/sec2. Where exceptional accuracy is required, the acceleration due to gravity (in cm/sec2) at variousplaces on the surface of the Earth can be found from Helmert’s equation: g = 980.616 – 2.5928 cos (2φ) + 0.0069 cos2 (2φ) – 3.086×10-6 H,where φ is the latitude and H is the elevation above sea level in centimeters.