Liquids variation with temperature

Tables 23-26 show the variation with temperature of some relevant physical properties of liquid sodium.

The dipole moment of a molecule can be obtained from a measurement of the variation with temperature of the dielectric constant of a pure liquid or gaseous substance. In an electric field, as between the electrostatically charged plates of a capacitor, polar molecules tend to orient themselves, each one pointing its positive end toward the negative plate and its negative end toward the positive plate. This orientation of the molecules partially neutralizes the applied field and thus increases the capacity of the capacitor, an effect described by saying that the substance has a dielectric constant greater than unity (80 for liquid water at 20°C). The dipole moments of some simple molecules can also be determined very accurately by microwave spectroscopy. 

Linewidths Figure 1 shows the variation with temperature of the l C-NMR spectrum of 1-butene adsorbed on NaGeX zeolite at a surface coverage of 0= 0.5 while Table II reports the linewidth (AH at half intensity) variations for gaseous, liquid and adsorbed 1-and trans 2-butene molecules. 

In any discussion of solubility, it is important to remember solubility is temperature dependent. Generally, the solubility of solids in liquids increases with temperature. The variation of solubility in water varies greatly for different solutes. Figure 11.2 demonstrates that the solubility may increase... 

Recently, Silver and Bray (52) were able to differentiate and to estimate the relative proportions of three- and four-coordinated borons in binary borate glasses. This technique was thus adopted by the present author in order to ascertain the presence or absence of four-coordinated boron in liquid B203 (35). Glassy samples were quenched in liquid mercury from temperatures up to 1400°C but no four-coordinated boron was detected. (The lower limit of detectability was estimated to be about 2%.) Experiments were also carried out on liquid B203 up to 500°C but again no four-coordinated boron was found. It thus appeared that at least up to 500 or 600°C, the structural variation of liquid B203 with temperature is not primarily the result of a boron coordination change of from three to four. 

This involves application of Equation (5.35), following Briant and Cuiec s method (1972), and is straightforward with immersion liquids for which parameter k is already known water, heptane, cyclohexane, benzene and paraxylene (cf. Table 5.1). Otherwise, it needs to be calculated from y(LG) and its variation with temperature (cf. Equation (5.34)). This approach was successfully used by Schultz et al. (1977) and, more recently, by Douillard et al. (1995). 

Estimation of gas-liquid mass-transfer rates also requires the knowledge of solubilities of absorbing and/or desorbing species and their variations with temperature (i.e., knowledge of heats of solution). In some reactions, such as hydrocracking, significant evaporation of the liquid occurs. The heat balance in a hydrocracker would thus require an estimation of the heat of vaporization of the oil as a function of temperature and pressure. The data for the solubility, heat of solution, and heat of vaporization for a given reaction system should be obtained experimentally if not available in the literature. 

Likewise, the heat capacity values tabulated in the present compilation may appear different from those of other compilations, even when the original data are the same. This is due to the fact that the original measurements are usually heat content measurements at high temperatures and the accuracy of the heat content measurements is not sufficient to allow the temperature dependence to be fixed explicitly. Different people assume different functions to represent the temperature variation of the heat content or heat capacity. For example, some prefer to take an average constant heat capacity to represent data for a limited liquid range. Others will assume a linear variation with temperature with some relationship between the two coefficients of the heat capacity equation. 

The use of the foregoing definition of an ideal solution implies certain properties of such a solution. The variation of the fugacity / of a pure liquid i with temperature, at constant pressure and composition, is given by equation (29.22), viz.. 

The volume occupied by a given mass of liquid varies with temperature, as does the device that holds the liquid during measurement. Most volumetric measuring devices are made of glass, which fortunately has a small coefficient of expansion. Consequently, variations in the volume of a glass container with temperature need not be considered in ordinary analytical work. 

A different approach was made by Dyre et al. (1996) to account for the experimental viscosity variations with temperature as an alternative to VTF and AG models. They considered the flow in viscous liquids to arise from sudden events involving motion and reorganization of several molecules. From the viewpoint of mechanism, the energy required for such flow is minimized if the surrounding liquid is shoved aside to create the necessary volume for rearrangement. This volume is fundamentally different from the volume of the free volume theory and is, in principle, an activation volume. The free energy involved may be written as... 

The viscosities of liquids decrease with temperature. Also, the variation is linear over a wide range of temperatures from the freezing point to the boiling point. This is expressed by the Andrade correlation [7],... 

At temperatures below the boiling point, which is ViT, the total surface energy and the energy of evaporation are nearly constant. The surface tension, y, variation with temperature is given in Figure 3.6 for different liquid n-alkanes with a number of carbon atoms from 5 (C5) to 18 (C,g). ... 

The effect of large changes in pressure at constant temperature on the viscosity of various hydrocarbons is shown in Figure 3. There we see that the logarithm of the viscosity of liquid hydrocarbons and hydrocarbon mixtures increases almost linearly with increasing pressure. Alternatively, viscosity can be considered to be a function of density rather than pressure, and this is used in several of the models discussed later. The kinematic viscosity shows similar trends with respect to these variables mentioned above, however its variation with temperature is significantly more linear than dynamic viscosity so that the former is somewhat easier to correlate than the latter. Consequently, some correlations have been developed exclusively for the kinematic viscosity, as will be discussed later. 

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