Liquid-Vapor Phase Change

The slope of the line allows for the determination of the enthalpy of vaporization of water, A//Vap, and the y intercept yields the entropy of vaporization, A. S vap As both the enthalpy and the entropy of water increase as the phase change liquid — vapor occurs, the slope and y intercept of the Clausius-Clapeyron equation are negative and positive, respectively. At 373 K these thermodynamic quantities have values of AHvap = 40.657 kJ mol-1 and ASvap = 109.0 J K-1 mol-1. The leavening action due to water vapor or steam arises from the increased amount of water vapor that forms as pastry temperatures initially rise in the oven and then from the increased volume of the water vapor as temperatures continue... 

The pressure-temperature phase diagrams also serve to highlight the fact that the polymorphic transition temperature varies with pressure, which is an important consideration in the supercritical fluid processing of materials in which crystallization occurs invariably at elevated pressures. Qualitative prediction of various phase changes (liquid/vapor, solid/vapor, solid/liquid, solid/liquid/vapor) at equilibrium under supercritical fluid conditions can be made by reference to the well-known Le Chatelier s principle. Accordingly, an increase in pressure will result in a decrease in the volume of the system. For most materials (with water being the most notable exception), the specific volume of the liquid and gas phase is less than that of the solid phase, so that... 

The vaporization process describes the phase change liquid (1) gas (g), so from the definition of AH we can write... 

This is the fundamental distillation equation, often referred to as the Rayleigh law when in its integrated form (Rayleigh, 1896). As far as Dt is considered to be a function of F, this equation applies to the change of any species concentration in the course of phase separation. Liquid-vapor or solid-solid fractionations are liable to the same formulation. 

Ideal gas enthalpy, Hfv> is obtained from (4-60). The derivative of pure component liquid fugacity coefBcient with respect to temperature leads to the following relation for combined effects of pressure and latent heat of phase change from vapor to liquid. 

It is hard to find out much about internal holdup. Presumably this will be determined by the internal void fraction of the catalyst, which one may assume is totally filled with liquid phase—at least for reactions in which no phase change to vapor occurs. 

The function p(v) at fixed temperature (the isotherm) is shown in Fig. 5.1. The curves 1, 2, 3 correspond to different temperatures. The curve 3 corresponds to a temperature above the critical temperature (T > T ). In this state the curve changes smoothly, pressure falls with increase of o, and the substance can be in equilibrium only in the gaseous form. The second curve corresponds to the critical temperature It is the highest temperature at which liquid and vapor states can coexist in balance with each other. At temperature T < Ti (curve 1) the dependence p o) is non-monotonous. To the left of the point B (line AB) the substance is in the mono-phase liquid state, to the right of point G (line GH) the substance is in the mono-phase vapor state. The region between points B and G corresponds to the equilibrium the bi-phase state liquid - vapor. In accordance with the Maxwell s rule, squares of areas BDE and EFG are equal. From the form of isotherms it follows that in pre-critical area (T < Tc) the cubic equation... 

Evaporation (also known as vaporization) is the phase change from liquid to vapor. Condensation is the phase change from vapor to liquid. In a closed system, when vaporization and condensation are occurring at the same rate, a state of dynamic equilibrium exists and the vapor pressure is equal to the equilibrium vapor pressure. Vapor pressure measures how easily molecules escape to the vapor phase. A volatile substance has a high vapor pressure. 

Vaporizing Liquids Certain liquids vaporize with heat (think of steam), and other lit]uids vaporize with a drop in pressure (think of liquid propane or freon). To eontrol vaporizing liquids so they don t change phase in the seal chamber. 

Boiling point The temperature at which the vapor pressure of a liquid is equal to the external pressure, and the liquid changes phase into the vapor state. 

Latent heat The quantity of heat that is absorbed or released in an isothermal transformation of phase, in kj kg C b Latent heat of vaporization The heat added during an isothermal change of phase from liquid to gas. 

Notice from the figure that the effect of temperature on entropy is due almost entirely to phase changes. The slope of the curve is small in regions where only one phase is present. In contrast, there is a large jump in entropy when the solid melts and an even larger one when the liquid vaporizes. This behavior is typical of all substances melting and vaporization are accompanied by relatively large increases in entropy. 

We have encountered equilibrium before—in our we considered the liquid-gas equilibrium that consideration of phase changes. In Section 5-1.2 fixes the vapor pressure of a liquid, and in Sec-142... 

A triple point is a point where three phase boundaries meet on a phase diagram. For water, the triple point for the solid, liquid, and vapor phases lies at 4.6 Torr and 0.01°C (see Fig. 8.6). At this triple point, all three phases (ice, liquid, and vapor) coexist in mutual dynamic equilibrium solid is in equilibrium with liquid, liquid with vapor, and vapor with solid. The location of a triple point of a substance is a fixed property of that substance and cannot be changed by changing the conditions. The triple point of water is used to define the size of the kelvin by definition, there are exactly 273.16 kelvins between absolute zero and the triple point of water. Because the normal freezing point of water is found to lie 0.01 K below the triple point, 0°C corresponds to 273.15 K. 

Carey van P (1992) Liquid-vapor phase-change phenomena. An introduction to the thermophysics of vaporization and condensation processes in heat transfer equipment. Hemisphere, New York Celata GP, Cumo M, Mariani A (1997) Experimental evaluation of the onset of subcooled flow boiling at high liquid velocity and subcoohng. Int J Heat Mass Transfer 40 2979-2885 Celata GP, Cumo M, Mariani A (1993) Burnout in highly subcooled water flow boiling in small diameter tubes. Int J Heat Mass Transfer 36 1269-1285 Chen JC (1966) Correlation for boiling heat transfer to saturated fluids in convective flow. Ind Eng Chem Process Des Develop 5 322-329... 

The temperature distribution has a characteristic maximum within the liquid domain, which is located in the vicinity of the evaporation front. Such a maximum results from two opposite factors (1) heat transfer from the hot wall to the liquid, and (2) heat removal due to the liquid evaporation at the evaporation front. The pressure drops monotonically in both domains and there is a pressure jump at the evaporation front due to the surface tension and phase change effect on the liquid-vapor interface. 

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