Vaporization, heat saturation

Equations for Hadacher vapor pressure, vapor heat capacity, saturated Hquid volume, and Hquid viscosity can be found in Refs. 34 and 41. 

This equation follows from equation 66, because vaporization occurs at the constant pressure Moreover, the heat of vaporization is related to the slope of the vapor—Hquid saturation curve through the Clapeyron equation ... 

Enthalpy of Vaporization The enthalpy (heat) of vaporization AHv is defined as the difference of the enthalpies of a unit mole or mass of a saturated vapor and saturated liqmd of a pure component i.e., at a temperature (below the critical temperature) anci corresponding vapor pressure. AHy is related to vapor pressure by the thermodynamically exact Clausius-Clapeyron equation ... 

The boiling of water results in the continuous absorption of heat energy until a point is reached, for any particular pressure, at which the liquid (water) changes into a gas (steam). This boiling point or (heat) saturation temperature occurs when the water vapor pressure is equal to the local pressure. 

In this table the parameters are defined as follows Bo is the boiling number, d i is the hydraulic diameter, / is the friction factor, h is the local heat transfer coefficient, k is the thermal conductivity, Nu is the Nusselt number, Pr is the Prandtl number, q is the heat flux, v is the specific volume, X is the Martinelli parameter, Xvt is the Martinelli parameter for laminar liquid-turbulent vapor flow, Xw is the Martinelli parameter for laminar liquid-laminar vapor flow, Xq is thermodynamic equilibrium quality, z is the streamwise coordinate, fi is the viscosity, p is the density, <7 is the surface tension the subscripts are L for saturated fluid, LG for property difference between saturated vapor and saturated liquid, G for saturated vapor, sp for singlephase, and tp for two-phase. 

The actual vapor heat pump cycle deviates from the ideal cycle primarily because of inefficiency of the compressor, pressure drops associated with fluid flow and heat transfer to or from the surroundings. The vapor entering the compressor must be superheated slightly rather than a saturated vapor. The refrigerant entering the throttling valve is usually compressed liquid rather than a saturated liquid. 

Superheating Heating of a vapor, particularly saturated steam to a temperature much higher than the boiling point at die existing pressure occurs in power plants to improve efficiency and to reduce condensation in the turbines. 

When Eq. (4.11) is applied to the vaporization of a pure liquid, dPM/ dT is the slope of the vapor pressure-vs.-temperature curve at the temperature of interest, AV is the diffeVence between molar volumes of saturated vapor and saturated liquid, and AH is the latent heat of vaporization. Thus values of AH may be calculated from vapor-pressure and volumetric data. 

Liquid water at 325 K and 8000 kPa flows into a boiler at tlie rate of 10 kg s and is vaporized, producing saturated vapor at 8000 kPa. What is tlie maximum fraction of the heat added to the water in the boiler that can be converted into work in a process whose product is water at initial conditions, if Ftr = 300 K What happens to the rest of the heat What is the rate of entropy change in the surroundings as a result of the work-producing process In the system Total ... 

Vapor pressure data, as reviewed by Brewer and Kane 37), can be represented by assuming the tetratomic molecule to be the gaseous species, with a heat of sublimation at 298 K. of 34,500 cal./mole, an entropy at 298 K. of 75.00 e. u., and a reasonable estimate of the heat capacity. According to this view, there is no appreciable concentration of the diatomic species in the vapor at saturation pressure below 1000 K., which sets a lower limit of about 48,000 cal./mole for the heat of sublimation at 298 K. for the diatomic gas. Comparison with the bond energies of P4 and Sb4 gives support to this value. 

Steam and other vapor heating systems are inherently safe, as the temperature cannot exceed the saturation temperature at the supply pressure. Other heating systems rely on control of the heating rate to limit the maximum process temperature. Electrical heating systems can be particularly hazardous, since the heating rate is proportional to the resistance of the heating element, which increases with temperature. 

Vertical Surfaces. Condensation heat transfer coefficients for external condensation on vertical surfaces depend on whether the vapor is saturated or supersaturated the condensate film is laminar or turbulent and the condensate film surface is wave-free or wavy. Most correlations assume a constant condensation surface temperature, but variable surface temperature conditions are correlated as well as summarized in Table 17.23. All coefficients represent mean values (over a total surface length), that is, h = (1/L) 10 hloc dx. 

The latent heat of vaporization per unit mass of a pure substance at a given temperature, X, is defined as the difference in enthalpy between the saturated vapor and saturated liquid at the given temperature, T. Since enthalpy is a thermodynamic function of state, show that X can be evaluated from a known value of X0 at a reference temperature T0 from the equation... 

These same arguments may be applied to the case of a moist atmosphere. Because of the release of the latent heat of vaporization, a saturated parcel cools on rising at a slower rate than a dry parcel, since... 

LATENT HEAT OF VAPORIZATION - The energy required to produce saturated vapor from saturated liquid at constant pressure per unit mass of fluid. 

Vw and Vl are the specific molar volumes of saturated vapor and saturated liquid, respectively AHy is the molar latent heat of vaporization... 

Condensation of saturated vapor to saturated liquid. The heat for this part is the negative of the heat of vaporization ... 

In the two-phase region, vapor and liquid coexist, and vapor and liquid have the same temperature (thermal equilibrium) and pressure (mechanical equilibrium). When they are in equilibrium with each other, vapor and liquid are called saturated vapor and saturated liquid, respectively. If a saturated liquid is further heated at constant pressure, the temperature does not rise any more but stays constant. Instead, vapor is generated until all liquid is vaporized. Similarly, if saturated vapor is cooled down, the temperature stays constant, and the vapor condenses and forms a saturated liquid. Figure 2.8 illustrates the well-known behavior of water at P = 1.013 bar, when it is heated up from = 50 to 1 2 = 150 C. 

The force field for ethanol [252] consists of three LJ 12-6 sites plus three point charges and was parameterized to ab initio and experimental data. The nucleus positions of aU ethanol atoms were computed by QM at the HF level of theory with a 6-3IG basis set. This force field is also based on the anisotropic approach of Ungerer et al. [130]. The LJ parameters and the anisotropic offset were fitted to experimental saturated liquid density, vapor pressure, and enthalpy of vaporization. The simulation results from this ethanol force field deviate on average from experimental values of vapor pressure, saturated liquid density, and heat of vaporization by 3.7, 0.3, and 0.9%, respectively. 

Theoretical analysis of filmwise condensation of a stationary pure saturated vapor was originally presented by Nusselt (1916) for vertical surface (Figure 22.24). This analysis assumed laminar flow and constant properties for liquid film, no shear stress at the liquid-vapor interface, vapor at saturation temperature, and heat transfer through the film by conduction only. 

Temperature control is essential and is achieved by boiling a hydrocarbon heat transfer fluid on the outside of the reactor tubes. This vaporized fluid is then condensed in a heat exchanger by transferring heat to a stream of saturated liquid water at 100 bar to produce saturated stream at 100 bar. The reactor feed is 11% C2H4, 13% O2 and the rest N2 at 360°C at 10 bar. The reactor product stream is at 375°C and 10 bar and the conversion of C2H4 is 22% with a 83% selectivity for C2H4O. At the operating pressure used in this system, the heat transfer fluid boils at 350°C with a heat of vaporization of 500 Btu/lb and has a liquid heat capacity of 0.8 Btu/lb °C and a vapor heat capacity of 0.4 Btu/lb °C. The flow of heat transfer fluid is adjusted so that it enters the reactor as liquid at 340°C and leaves as a two-phase mixture with vapor fraction of 21% (see Fig. P2.31). 

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