Temperature dependence of the density

Chlorine, a member of the halogen family, is a greenish yellow gas having a pungent odor at ambient temperatures and pressures and a density 2.5 times that of air. In Hquid form it is clear amber SoHd chlorine forms pale yellow crystals. The principal properties of chlorine are presented in Table 15 additional details are available (77—79). The temperature dependence of the density of gaseous (Fig. 31) and Hquid (Fig. 32) chlorine, and vapor pressure (Fig. 33) are illustrated. Enthalpy pressure data can be found in ref. 78. The vapor pressure P can be calculated in the temperature (T) range of 172—417 K from the Martin-Shin-Kapoor equation (80) ... 

It is not the purpose of chemistry, but rather of statistical thermodynamics, to formulate a theory of the structure of water. Such a theory should be able to calculate the properties of water, especially with regard to their dependence on temperature. So far, no theory has been formulated whose equations do not contain adjustable parameters (up to eight in some theories). These include continuum and mixture theories. The continuum theory is based on the concept of a continuous change of the parameters of the water molecule with temperature. Recently, however, theories based on a model of a mixture have become more popular. It is assumed that liquid water is a mixture of structurally different species with various densities. With increasing temperature, there is a decrease in the number of low-density species, compensated by the usual thermal expansion of liquids, leading to the formation of the well-known maximum on the temperature dependence of the density of water (0.999973 g cm-3 at 3.98°C). 

Kumar, A. Temperature dependence of the densities and speeds of sound of the binary solutions of LiC104 with diethyl ether, tetrahydrofuran, acetone, and ethyl acetate, J. Chem. Eng. Data, 45(4) 630-635, 2000. 

Although most physical properties (e.g., viscosity, density, heat conductivity and capacity, surface tension) must be regarded as variable, it is particularly the value of viscosity that can be varied by many orders of magnitude under certain process conditions [5,11]. In the following, dimensional analysis will be applied, via examples, to describe the temperature dependency of the density und viscosity of non-Newtonian fluids as influenced by the shear stress. 

Figure 4 (A) Temperature dependency of the density, p(T), for four different liquids. (B)...

Convection in Melt Growth. Convection in the melt is pervasive in all terrestrial melt growth systems. Sources for flows include buoyancy-driven convection caused by the solute and temperature dependence of the density surface tension gradients along melt-fluid menisci forced convection introduced by the motion of solid surfaces, such as crucible and crystal rotation in the CZ and FZ systems and the motion of the melt induced by the solidification of material. These flows are important causes of the convection of heat and species and can have a dominant influence on the temperature field in the system and on solute incorporation into the crystal. Moreover, flow transitions from steady laminar, to time-periodic, chaotic, and turbulent motions cause temporal nonuniformities at the growth interface. These fluctuations in temperature and concentration can cause the melt-crystal interface to melt and resolidify and can lead to solute striations (25) and to the formation of microdefects, which will be described later. 

It can be seen that the prediction is in satisfactory agreement with experimental observations [27]. The temperature dependence of the density of condensed electrons is shown in Figure 7 which has utilised the thermal average of the density of condensed electrons obtained as described above. 

The essential difference between the multistate and the continuum model rests upon the temperature dependence of the density of states (Fig. 13). An experimental distinction between the models may also be possible (21) from a study of genuine vitreous (quick-frozen) solutions, i.e., systems that, at low temperature, retain the appropriate fluid solution species existing at the freezing point. For these systems, the continuum model predicts a single species at low temperature with a low A value, while the multistate picture requires the superposition of spectra from two (or more) species one (or more) in high abundance with a low A value, and at least one in lower abundance with a high value of A (Fig. 13). 

Example 12 Standard representation of the temperature dependence of the density... 

The electrolyte density is very important in order to obtain a good separation between melt and metal and to avoid the risk of mixing bath and metal. The density of molten cryolite has been measured by several authors [162-167], According to Edwards et al. [164] the temperature dependence of the density of cryolite is given by... 

Gopal and Rizvi83) have used the temperature dependence of the density to determine an approximate value of 690 °K for the critical temperature of NMA. 

When water is mixed with another liquid, the number of bonds can increase, as, for instance, in water-ethanol solutions (structure formers) or decrease (structure breakers). However, in all cases, the tetrahedral structure vanishes (except, of course, for isotopic mixtures of light and heavy water). As a consequence, the anomalies of liquid water are strongly reduced upon addition of other components. For instance, 7% of ethanol is sufficient to completely suppress the maximum in the temperature dependence of the density of the mixture [9]. 

Figure 8 shows the temperature dependence of the density (g/mL) of an Indian edible sunflower oil [based on Subrahmanyam et al. (27)]. 

Figure 8. Temperature dependence of the density (g/cc) of an Indian edibie sunflower oii [based on (27)1...

The density based characteristic number K and other such numbers Kgl, Kg2,... characterise the dimensionless temperature dependence of the density ... 

Provided that the temperature differences are not too large the temperature dependence of the density can be determined by the product of the expansion coefficient p0 and a characteristic temperature difference A00. One density based characteristic group is sufficient for this case, namely... 

The density variation due to the temperature generates a buoyancy force in the gravitational field. However, this has little influence on the other forces, including inertia and friction, which affect the fluid particles. As a good approximation it is sufficient to consider the temperature dependence of the density in buoyancy alone. This assumption is known as the Boussinesq-Approximation8. A characteristic (volume related) lift force is... 

In the interesting case where the Fermi energy is in the gap but its distance from the nearest band is not very large, this band may be thermally populated. This leads to a characteristic temperature dependence of the density of mobile charge carriers... 

Figure 1. Temperature dependencies of the density and specific volume of dry elastin (O) native (%) purified.

The temperature dependence of the density of dry samples of native and purified elastin is shovm in Figure 1. In the temperature range explored, the native protein shows a higher density than the purified one, typical values being 1.245 g/ml and 1.232 g/ml, respectively, at 25 C. In a first approximation, this difference in density can be accounted for by the different composition of the native and purified protein. If native elastin is considered a two phase composite material (approximately 80% elastin and 20% collagen), disregarding other minor components whose density data are not available, the density of the composite can be calculated from the equation ... 

Another fact that has been ignored here is the temperature dependence of the density-of-states parameter itself. Based on the temperature dependence of the optical absorption tail (see, for example, Cody cf a/., 1981 a), this quantity may deviate from its average value by 10% over the temperature range of interest. Better data and more understanding are needed before this effect can be included in the transport model in a meaningful way. 

The experimental data of Gu and Brennecke [131] are shown for comparison. Clearly, the all-atom model matches the data extremely well, especially considering that the model was not adjusted to fit the experimental results. As expected, the simplest united atom model (UAl) overestimates the density by about 5%, but the other united atom model actually underestimates the density by about the same amount. Interestingly, all three models capture the temperature dependence of the density reasonably well. For example, the volume expansivity obtained using the aU-atommodelisap = 5.5 x while the experimental value [128] is a p = 6.1 x... 

Sink-float methods are commonly used for quality control measurements for glasses. A sample is placed into a test tube containing an organic liquid which is slightly more dense than the sample. The tube is heated until the density of the liquid becomes less than that of the sample, whereupon the sample will begin to sink. If the test tube also contains a standard of known density, the difference in temperature at which the sample and standard sink can be used to calculate the difference in their densities, provided the temperature dependence of the density of the liquid is known. This method is capable of detecting differences in density of as little as 20 ppm. 

Ge(C2H5)4 is a colorless oily liquid having a pleasant characteristic odor somewhat suggestive of the lighter aliphatic hydrocarbons [1]. Experimental values of the density [1, 2, 3, 7, 34, 41, 42] are given in Fig. 2. The temperature dependence of the density is expressed by the following equations ... 

Ge(C4H9)4 is a colorless, oily, and almost odorless liquid [1]. Selected measured values of the density [44] and equations for the temperature dependence of the density [44, 57] are given below ... 

The temperature dependence of the density is given by the following equations ... 

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