Kelvin

Joule-Thomson effect, Joule-Kelvin effect... 

Kelvin scale See absolute temperature. kephaUn See cephalins. 

T being the boiling temperature (Kelvin) and S being tbe standard specific gravity (15.6°C/15.6°C). Refer to Chapter 4. 

The wavelength of ripples on the surface of a deep body of liquid depends on the surface tension. According to a formula given by Lord Kelvin [97],... 

Here, r is positive and there is thus an increased vapor pressure. In the case of water, P/ is about 1.001 if r is 10" cm, 1.011 if r is 10" cm, and 1.114 if r is 10 cm or 100 A. The effect has been verified experimentally for several liquids [20], down to radii of the order of 0.1 m, and indirect measurements have verified the Kelvin equation for R values down to about 30 A [19]. The phenomenon provides a ready explanation for the ability of vapors to supersaturate. The formation of a new liquid phase begins with small clusters that may grow or aggregate into droplets. In the absence of dust or other foreign surfaces, there will be an activation energy for the formation of these small clusters corresponding to the increased free energy due to the curvature of the surface (see Section IX-2). 

While Eq. III-18 has been verified for small droplets, attempts to do so for liquids in capillaries (where Rm is negative and there should be a pressure reduction) have led to startling discrepancies. Potential problems include the presence of impurities leached from the capillary walls and allowance for the film of adsorbed vapor that should be present (see Chapter X). There is room for another real effect arising from structural peiturbations in the liquid induced by the vicinity of the solid capillary wall (see Chapter VI). Fisher and Israelachvili [19] review much of the literature on the verification of the Kelvin equation and report confirmatory measurements for liquid bridges between crossed mica cylinders. The situation is similar to that of the meniscus in a capillary since Rm is negative some of their results are shown in Fig. III-3. Studies in capillaries have been reviewed by Melrose [20] who concludes that the Kelvin equation is obeyed for radii at least down to 1 fim. 

With the preceding introduction to the handling of surface excess quantities, we now proceed to the derivation of the third fundamental equation of surface chemistry (the Laplace and Kelvin equations, Eqs. II-7 and III-18, are the other two), known as the Gibbs equation. 

The Kelvin equation (Eq. HI-18), which gives the increase in vapor pressure for a curved surface and hence of small liquid drops, should also apply to crystals. Thus... 

Bikerman [179] has argued that the Kelvin equation should not apply to crystals, that is, in terms of increased vapor pressure or solubility of small crystals. The reasoning is that perfect crystals of whatever size will consist of plane facets whose radius of curvature is therefore infinite. On a molecular scale, it is argued that local condensation-evaporation equilibrium on a crystal plane should not be affected by the extent of the plane, that is, the crystal size, since molecular forces are short range. This conclusion is contrary to that in Section VII-2C. Discuss the situation. The derivation of the Kelvin equation in Ref. 180 is helpful. 

This section represents a continuation of Section VII-5, which dealt primarily with the direct estimation of surface quantities at a solid-gas interface. Although in principle some of the methods described there could be applied at a solid-liquid interface, very little has been done apart from the study of the following Kelvin effect and nucleation studies, discussed in Chapter IX. 

Most studies of the Kelvin effect have been made with salts—see Refs. 2-4. A complicating factor is that of the electrical double layer presumably present Knapp [3] (see also Ref. 6) gives the equation... 

Fig. XVII-1. Adsorption of N2 on rutile temperatures indicated are in degrees Kelvin. (a) Low-pressure region (b) high-pressure region. (From Ref. 1.).

Derive Eq. XVII-136. Derive from it the Kelvin equation (Eq. Ill-18). 

One might expect the frequency factor A for desorption to be around 10 sec (note Eq. XVII-2). Much smaller values are sometimes found, as in the case of the desorption of Cs from Ni surfaces [133], for which the adsorption lifetime obeyed the equation r = 1.7x 10 exp(3300// r) sec R in calories per mole per degree Kelvin). A suggested explanation was that surface diffusion must occur to desorption sites for desorption to occur. Conversely, A factors in the range of lO sec have been observed and can be accounted for in terms of strong surface orientational forces [134]. 

R is the gas constant per mole, while K is the temperature unit Kelvin). The dashed lines represent metastable extensions of the stable phases beyond the transition temperatures. 

In the dense interstellar medium characteristic of sites of star fonuation, for example, scattering of visible/UV light by sub-micron-sized dust grains makes molecular clouds optically opaque and lowers their internal temperature to only a few tens of Kelvin. The thenual radiation from such objects therefore peaks in the FIR and only becomes optically thin at even longer wavelengths. Rotational motions of small molecules and rovibrational transitions of larger species and clusters thus provide, in many cases, the only or the most powerfiil probes of the dense, cold gas and dust of the interstellar medium. 

Molecular beam sample introduction (described in section (Bl.7.2)). followed by the orthogonal extraction of ions, results in improved resolution in TOP instruments over eflfrisive sources. The particles in the molecular beam typically have translational temperatures orthogonal to the beam path of only a few Kelvin. Thus, there is less concern with both the initial velocity of the ions once they are generated and with where in the ion source they are fonned (since the particles are originally confined to the beam path). 

This equation describes the additional amount of gas adsorbed into the pores due to capillary action. In this case, V is the molar volume of the gas, y its surface tension, R the gas constant, T absolute temperature and r the Kelvin radius. The distribution in the sizes of micropores may be detenninated using the Horvath-Kawazoe method [19]. If the sample has both micropores and mesopores, then the J-plot calculation may be used [20]. The J-plot is obtained by plotting the volume adsorbed against the statistical thickness of adsorbate. This thickness is derived from the surface area of a non-porous sample, and the volume of the liquified gas. 

Historically, the first and most important capacitance method is the vibrating capacitor approach implemented by Lord Kelvin in 1897. In this technique (now called the Kelvin probe), the reference plate moves relative to the sample surface at some constant frequency and tlie capacitance changes as tlie interelectrode separation changes. An AC current thus flows in the external circuit. Upon reduction of the electric field to zero, the AC current is also reduced to zero. Originally, Kelvin detected the zero point manually using his quadrant electrometer. Nowadays, there are many elegant and sensitive versions of this technique. A piezoceramic foil can be used to vibrate the reference plate. To minimize noise and maximize sensitivity, a phase-locked... 

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