Water density, variation with temperature

Hot-Water Process. The hot-water process is the only successflil commercial process to be appHed to bitumen recovery from mined tar sands in North America as of 1997 (2). The process utilizes linear and nonlinear variations of bitumen density and water density, respectively, with temperature so that the bitumen that is heavier than water at room temperature becomes lighter than water at 80°C. Surface-active materials in tar sand also contribute to the process (2). The essentials of the hot-water process involve conditioning, separation, and scavenging (Fig. 9). 

When the density variation with temperature of water is considered, a maximum is found to oceur near 4°C as discussed in Problem 8.14. Near this point of maximum, density is approximately given by ... 

Here, cs denotes the concentration in mol/kg (molality scale), and [s] is the concentration in mol/liter (molarity scale). Both units are related in that [s] = pwcs where pw= 1 kg/dm3 is the density of water. Its variation with temperature causes the molarity scale to depend on temperature, whereas the molality scale does not. In the temperature range 0-25°C, however, the density of water differs from unity by less than 0.3%, so that [s] = cs with reasonable accuracy. Most Henry coefficients are less well known. From the definitions in Eqs. (8-7) and (8-8), the coefficients involved are related by... 

FIGURE 5.50 The variation of the densities of water and tetrachloromethane with temperature. Note that ice is less dense than water at its freezing point and that water itself has its maximum density at 4°C. 

The basic properties of water such as viscosity, dissociation constant, dielectric constant, compressibility, and the coefficient of thermal expansion play a major role in determining optimal reaction conditions for obtaining maximum benefits in both SCWO and WAO processes. The properties of water change dramatically with temperature, particularly near the critical point [24-26]. A well-known example, the variation of pAw with temperature at the saturation pressure, is shown in Fig. 3. The dissociation constant of water goes through a maximum around 250°C (pAw minimum), and then undergoes a sharp decline as the temperature approaches the critical point. The density and the dielectric constant of water also show sharp changes close to the critical point, as shown in Fig. 4. 

We now turn attention to a completely different kind of supercritical fluid supercritical water (SCW). Supercritical states of water provide environments with special properties where many reactive processes with important technological applications take place. Two key aspects combine to make chemical reactivity under these conditions so peculiar the solvent high compressibility, which allows for large density variations with relatively minor changes in the applied pressure and the drastic reduction of bulk polarity, clearly manifested in the drop of the macroscopic dielectric constant from e 80 at room temperature to approximately 6 at near-critical conditions. From a microscopic perspective, the unique features of supercritical fluids as reaction media are associated with density inhomogeneities present in these systems [1,4],... 

The fluid viscosity and thermal conductivity experience the largest variation with temperature. Compared with the density and the specific heat variation, their influence on heat transfer is significantly higher, e.g. in the case of water. Therefore, density and thermal conductivity can in most cases be considered to be constant The fluid property variation becomes more important with decreasing diameter, where the axial variation is more pronounced than the variation over the cross-section of the channel. In contrast to the viscous dissipation, the significance of property variations increases with decreasing Br [53]. 

The variation of the viscosity, 17, of water with temperature and density is shown in Fig. 3b. The viscosity of water decreases sharply with temperature from 0 to 200°C, and then, gradually decreases further. However, the density dependence of viscosity is, by contrast, rather simple. 

Bitumen. There are wide variations both in the bitumen saturation of tar sand (0—18 wt % bitumen), even within a particular deposit, and the viscosity. Of particular note is the variation of density of Athabasca bitumen with temperature, and the maximum density difference between bitumen and water (70—80°C (160—175°F)) hence the choice of the operating temperature of the hot-water bitumen-extraction process. 

The reported densities of ionic liquids vary between 1.12 g cm for [(n-QHi7)(C4H9)3N][(CF3S02)2N] and 2.4 g cm for a 34-66 mol% [(CH3)3S]Br/AlBr3 ionic liquid [21, 23]. The densities of ionic liquid appear to be the physical property least sensitive to variations in temperature. For example, a 5 degree change in temperature from 298 to 303 K results in only a 0.3 % decrease in the density for a 50.0 50.0 mol % [EMIM]C1/A1C13 [17]. In addition, the impact of impurities appears to be far less dramatic than in the case of viscosity. Recent work indicates that the densities of ionic liquids vary linearly with wt. % of impurities. For example, 20 wt. % water (75 mol %) in [BMIM][BF4] results in only a 4 % decrease in density [33]. 

Why temperatures and rainfall near Chesapeake Bay should be affected by variations of the tidal forces is not so clear. However the atmosphere and stratosphere are pulled away from the earth by tidal forces just as are the waters of the earth. These forces vary by as much as 10 percent during the tidal periods [67] resulting in density variations in the stratosphere with the same periods the consequent density variations may affect the relative rates of stratospheric chemical reactions, causing disturbances of temperature and rainfall on the ground with the tidal periodicities. 

Let us illustrate this phenomenon with a practical example, the variation of oxygen and of nitrogen equilibrium solubilities with depth in the ocean [1]. For seawater, the density p depends on temperature and salinity, and it could vary from 1.025 to 1.035 g cm. For dissolved oxygen, V2 = 0.97 cm g in seawater at a water temperarnre near 25°C. If d is expressed in meters, then at the lower limit of the water density. Equation (21.17) becomes... 

Since the oceans comprise over 70% of the earth s surface area, the absorbed solar energy that is stored as latent heat of the oceans represents a very large potential source of energy. As a result of variation in the density of ocean water with temperature, the ocean water temperature is not uniform with depth. Warm surface ocean water with low density tends to stay on the surface and cold water with high density within a few degree of 4°C tends to settle to the depths of the ocean. In the tropics, ocean surface temperatures in excess of 25° C occur. The combination of the warmed surface water and cold deep water provides two different temperature thermal reservoirs needed to operate a heat engine called OTEC (ocean thermal energy conversion). Since the temperature difference of the OTEC between the heat source and the heat sink is small, the OTEC power plant cycle efficiency... 

It is worthwhile to discuss the components of the standard uncertainty of a volume measurement here. The repeatability may be independently assessed by a series of fill-and-weigh experiments with water at a controlled temperature (and therefore density) using a balance so that the uncertainty of weighing is small compared with the variation in volume. Although this may be instructive, if the whole analysis is repeated, say, ten times, then the repeatability of the use of the pipette, or any other volume measurement is part of the repeatability of the overall measurement. This shows the benefit, in terms of reaching the final estimate of measurement uncertainty more quickly, of lumping together uncertainty components. 

Since the variation of water density with temperature is extremely small, the relative temperature variation of kinematic viscosity and dynamic viscosity r w are approximately equal. 

Why are these equations represented by 4th order polynomials and not 2nd order curves given that the vertical variation of temperature and vapor fraction are well approximated by second order functions The simple answer is that the transition from condensing water vapor to liquid water above 0 °C to condensing water ice below -20 °C, and the attendant affect on the fractionation factor (Fig. 2), results in additional structure not captured by 2nd or 3rd order curves. Each of the equations fit their respective model output with an R2 > 0.9997. The lack of symmetry of the modeled uncertainty reflects asymmetry in the probability density function and particularly the long tail toward lower values of T relative to the mean (see Fig. 2 of Rowley et al. 2001). The effect of this long tail is well displayed in both Figure 5 and 7. 

Figure 2-11 Variation of specific gravity (density) of Athabasca bitumen and water with temperature.

The density of a substance is the mass per unit volume of the substance (kg/m, g/cm Ibm/ft, etc.) The specific volume of a substance is the volume occupied by a unit mass of the substance it is the inverse of density. Densities of pure solids and liquids are essentially independent of pressure and vary relatively slightly with temperature. Hie temperature variation may be in either direction the density of liquid water, for example, increases from 0.999868 g/cm at 0°C to 1.00000 g/cm at 3.98°C, and then decreases to 0.95838 g/cm at 100°C. Densities of many pure compounds, solutions, and mixtures may be found in standard references (such as Perry s Chemical Engineers Handbook pp. 2-7 through 2-47 and 2-91 through 2-120). Methods of estimating densities of gases and mixtures of liquids are given in Chapter 5 of this book. 

Figfure 1.3 Variation of the density of water with temperature and NaCl concentration at a constant pressure of 10 MPa (modified after Garven and Freeze, 1984a, American Journal of Science, Volume 284, Figure 4. Reprinted by permission of American Journal Science). 

In most of your work using liquids and solids, density will not change very much with pressure, but for precise measurements for common substances you can always look up in a handbook the variation of density with pressure. The change in density with temperature is illustrated in Fig. 1.1 for liquid water and liquid ammo-... 

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