Evaporation of a liquid

As p(v2—Vi) can generally be neglected in comparison with U2 — Ui, it follows from the increase of the vapour pressure with temperature that U2 must always be greater than Ui. 

This result could not have been obtained from thermodynamics alone. The kinetic theory of gases and Uquids, on the other hand, leads us to conclude that TJ TJxy as work must be done against the molecular forces when the volume is increased from Vg to (see the paragraph on the Joule-Thomson effect, p. 97, and see also p. 152). 

The calculation of the vapour pressure curve, i.e. of the value of p for any given value of T, can only be carried out by an integration. Thus we have 

The integration is, however, only possible when L and are known functions of the temperature. In general this is not the case, but we can obtain an approximate solution of the problem for temperatures which are much below the critical temperature. In this case the specific volume of the liquid is small in comparison with that of the gas, and we may assume that the vapour obeys the gas laws. We may then write 

By integration we obtain the vapour pressure of the liquid at low temperatures in the form  

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There are two approaches to explain physical mechanism of the phenomenon. The first model is based on the existence of the difference between the saturated vapor pressures above two menisci in dead-end capillary. It results in the evaporation of a liquid from the meniscus of smaller curvature ( classical capillary imbibition) and the condensation of its vapor upon the meniscus of larger curvature originally existed due to capillary condensation. 

At first we tried to explain the phenomenon on the base of the existence of the difference between the saturated vapor pressures above two menisci in dead-end capillary [12]. It results in the evaporation of a liquid from the meniscus of smaller curvature ( classical capillary imbibition) and the condensation of its vapor upon the meniscus of larger curvature originally existed due to capillary condensation. We worked out the mathematical description of both gas-vapor diffusion and evaporation-condensation processes in cone s channel. Solving the system of differential equations for evaporation-condensation processes, we ve derived the formula for the dependence of top s (or inner) liquid column growth on time. But the calculated curves for the kinetics of inner column s length are 1-2 orders of magnitude smaller than the experimental ones [12]. 

The factors that affect the evaporation process are concentration in the liquid, solubility, pressure, temperature, scaling, and materials of construction. An evaporator is a type of heat exchanger designed to induce boiling and evaporation of a liquid. The major types of evaporator are... 

Misalignment of the sample. For example, improper insertion or positioning of the sample can easily change the elevation of its surface by 0.01 cm and appreciably alter the measured intensity (8.17). Evaporation of a liquid sample can have a similar result. 

Now consider any reversible change which is not a cyclic change, as, for example, the expansion of a gas, or the evaporation of a liquid. 

According to Clausius the latent-heat of evaporation of a liquid is approximately a linear function of the temperature, and diminishes with rise of temperature (cf. 94) ... 

Thus, if we find how the electromotive force changes when the temperature of the cell is altered on open circuit, i.e., when no current is passing, we can at once calculate A, the latent heat, just as we can calculate the latent heat of evaporation of a liquid when we know the variation of its vapour pressure with temperature. Since E changes only slightly with T, we can evaluate dE... 

In some cases, such as the evaporation of a liquid at an approximately constant temperature or the dissolving of a highly soluble gas in a liquid, the interface concentration may be either substantially constant or negligible in comparison with that of the bulk. In such cases, die integral on the left-hand side of equation 10.158 may be evaluated directly to... 

The vaporization rate or source term, determined by Equation 3-12, is used in Equation 3-9 to estimate the concentration (in ppm) of a volatile in an enclosure resulting from evaporation of a liquid ... 

Alcohols are organic compounds that contain the OH functional group. In this experiment, you will determine the strength of intermolecular forces of alcohols by determining how fast various alcohols evaporate. The evaporation of a liquid is an endothermic process, absorbing energy from the surroundings. This means that the temperature will decrease as evaporation occurs. 

Kinetic fractionations can occur when there is incomplete isotopic exchange between the different phases present in a system. A thorough introduction to kinetic stable isotope fractionation theory is unfortunately beyond the scope of the present review. Flowever, it is useful to include a brief discussion of some basic aspects, particularly in comparison to equilibrium fractionation theory. A simple example of kinetic fractionation is the evaporation of a liquid water droplet into a vacuum, in this example FljO molecules entering the gas phase are physically removed from the vicinity of the droplet, so there is no chance for isotopic equilibration between vapor-phase molecules and the residual liquid. Isotopic fractionation in this case is determined by a one-way reaction path, and will not, in general, be the same as the fractionation in a system where vapor-phase molecules are able to equilibrate and exchange with the liquid. In other reactions, isotopic exchange is limited by an energy barrier—an... 

Certainly the condition in Eq. (74) is valid since there must be no accumulation of solute at the interface. But the condition for equilibrium at the interface in Eq. (75) may not be adequate for the description of many mass transfer processes. It is not, for example, difficult to imagine that in the evaporation of a liquid, the vaporization may take place so rapidly that the concentration of vapor just above the liquid surface is considerably less than the concentration corresponding to the equilibrium vapor pressure. The problem of obtaining a quantitative theoretical description of this process has been attacked by Schrage (S4), who has suggested several molecular theories for describing gas-liquid and gas-solid systems. 

Equation (113) is the basis for analyzing Stefan s method of measuring diffusion coefficients by observing the rate of evaporation of a liquid in a tube. At the liquid level (s = Zi) the partial pressure is taken to be pA1 [this assumes equilibrium at the interface (see Sec. II,D,4)] at the top of the tube (z = zi) component A is continually removed so that pAi = 0. This method has been discussed by Wilke (W9) and has been used by Lee and Wilke (L3) for obtaining diffusion coefficients in gaseous systems. 

A simple example of molecular transport for a three-species problem is illustrated here. Consider evaporation of a liquid into a high-aspect-ratio tube open to air. The diffusive transport of species entering the vapor through evaporation can be solved as a onedimensional two-point boundary-value problem. 

As an example, consider the isothermal evaporation of a liquid interface into an unbounded space, previously considered by Danckwerts (Dl). The governing equation is now... 

In flow situations, empirical analogies between mass and heat transfer are usually employed. For single-particle mass transfer, the boundary layer analysis for mass transfer is similar to that for heat transfer and thus is used for typical applications such as sublimation of a solid (e.g., naphthalene ball) or evaporation of a liquid drop falling in air. For a single sphere of diameter dp moving in a fluid, in terms of a boundary layer analysis analogous... 

The word refrigeration implies the maintenance of a temperature below that of the surroundings. This requires continuous absorption of heat at a low temperature level, usually accomplished by evaporation of a liquid in a steady-state flow process. The vapor formed may be returned to its original liquid state for reevaporation in either of two ways. Most commonly, it is simply compressed and then condensed. Alternatively, it may be absorbed by a liquid of low volatility, from which it is subsequently evaporated at higher pressure. Before treating these practical refrigeration cycles, we consider the Carnot refrigerator, which provides a standard of comparison. 

This if the continuous process involving evaporation of a liquid into its vapour by heating the liquid. This is followed by cooling and so condensing the vapour back to the liquid. It is used to extract a pure sample of a liquid (or solvent) from an impure mixture, e.g pure water from dirty water or making pure alcohol from a fermented mixture. 

Another early theory, which also attracted a great deal of attention, was the ink-bottle theory this was originally put forward by Kraemer (1931) and subsequently developed by McBain (1935). Kraemer pointed out that the rate of evaporation of a liquid in a relatively large pore is likely to be retarded if the only exit is through a narrow channel. This argument led Brunauer (1945) to conclude that the liquid in the pore cannot be in true equilibrium with its vapour during the desorption process and therefore it is the adsorption branch of the loop which represents thermodynamic reversibility. 

In some situations, an apparent decrease in the detection limit can occur when the analytical procedure includes a preliminary preconcentration (e.g., by extraction or evaporation of a liquid sample). For example, if direct determination by atomic absorption spectrometry allows detection of 0.1 ng/mL metal in solution, then an increase in concentration after separation/preconcentration in the ratio 1 20 lowers the detection limit for the whole procedure to 0.005 ng/mL. Both values are useful and have real meaning when they are correctly described. 

How does each of the following affect the rate of evaporation of a liquid in an open dish ... 

The usual method of achieving low temperatures involves the evaporation of a liquid. This process, the change of a substance from... 

The mechanism of evaporation of a liquid depends on the relative values of the vapor pressure of the liquid and the total system pressure. If evaporation takes place at a temperature such that p < P, the process involves transfer of molecules from the surface of the liquid to the gas above the surface, while if p = P, vapor bubbles form throughout the entire liquid, but predominantly at the heated container walls that is, the liquid boils. The temperature at which p = Pis the boiling point of the liquid at the given pressure. 

In physical as well as chemical processes, the effect of entropy is to motivate reactions, even those where an input of energy may be required. A classical example is the evaporation of a liquid such as water or alcohol. The indication that the process requires energy is the cool feeling of the skin when water or alcohol evaporates. The water or alcohol... 

Figure 9. Particle Image Velocimetry (PFV) measurement during the evaporation of a liquid in a capillary tube, ID=200 pm [11]...

This equation was first obtained by Clapeyron, a French engineer who continued the work of Carnot. He derived the equation for the evaporation of a liquid. In its general form it was established by Clausius, and is therefore called the Clausius-Clapeyron, or briefly the Clausius equation. By means of this equation we can calculate the change in pressure dp produced by an arbitrary change in temperature dT from the quantities L, 2, Vj, and T, which can all be determined by experiment. 

Finally, we can deduce equation (3), without using thermodynamic functions (such as TJ or j/), by considering a reversible cycle. On p. 138 we found that the efficiency of such a cycle was equal to the temperature drop dT divided by the temperature T of the soirrce of heat. Consider the following cycle (for simplicity the evaporation of a liquid is taken as an example of the method) ... 

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