Modified latent heat of vaporization

Other propeities axe as listed before in connection with Eq. 10-2, We used a modified latent heat of vaporization in Eq. lO-.l to account for the heat tran.s-fet as.sociated with the superheating of the vapor. 

Theoretically the enthalpy-composition method is more exact than the use of the modified latent heats of vaporization, but in most cases the two agree within the accuracy of the calculation. For binary mixtures, if the necessary enthalpy data are already available, the enthalpy-composition method is the easier to apply if the data are not available and must be calculated, then the other method is the more convenient. For multicomponent mixtures the modified latent heat method is more convenient even if the complete enthalpy data are available. 

Thomas presented an interesting paper (2021) relating H bonding and viscosity, and he was quick to point out the approximate nature of his treatment. He combined a modification of Andrade s viscosity equation with a relation between vapor pressure and latent heat of vaporization and still another function relating the heat of H bonding with the degree of association. From these he calculated an approximate heat of vaporization and compared it to a nonassociated value from a modified Trouton rule equation. The difference is called... 

We can have a similar argument for vapor that enters the condenser as superheated vapor at a temperature 7,. instead of as saturated vapor. In this case the vapor must be cooled first to 3 , before it can condense, and this heat must be transferred to the wall as well. The amount of heat released as a unit mass of superheated vapor at a temperature 7,. is cooled to 75, is simply Cf,r[Ty - 7jjt), where Cp,. is the specific heat of the vapor at the average temperature of (Ty + 7sj,)/2. The modified latent heal of vaporization in this case becomes... 

HUMIDITY CHARTS FOR SYSTEMS OTHER THAN AIR-WATER. A humidity chart may be constructed for any system at any desired total pressure. The data required are the vapor pressure and latent heat of vaporization of the condensable component as a function of temperature, the specific heats of pure gas and vapor, and the molecular weights of both components. If a chart on a mole basis is desired, all equations can easily be modified to the use of molal units. If a chart at a pressure other than 1 atm is wanted, obvious modificatioi in the above equations may be made. Charts for several common systems besides air-water have been published. ... 

At a different point in the packed distillation column of Example 3.6, the methanol content of the bulk of the gas phase is 76.2 mol% that of the bulk of the liquid phase is 60 mol%. The temperature at that point in the tower is around 343 K. The packing characteristics and flow rates at that point are such that Fg = 1.542 x 10-3 kmol/m2-s and Fr = 8.650 x 10-3 kmol/m2-s. Calculate the interfacial compositions and the local methanol flux. To calculate the latent heat of vaporization at the new temperature, modify the values given in Example 3.6 using Watson s method (Smith et al., 1996) ... 

For horizontal tube, L is replaced by the tube diameter, D, and constant 0.943 becomes 0.725. An improvement to the Nusselt model was made by Rohsenow (1956) who considered the effects of subcooling within the liquid film and also allowed for a nonlinear distribution of temperature through the film due to energy convection. The latent heat of vaporization, / fg, was replaced by a modified form /zfg = /Zfg + 0.68Cpf(Tsat - Ts ) in the above equation. 

In this example, the use of the modified values did not make a large difference in the results, but if the design conditions had been nearer the optimum, e.gr., (Or/D) = 1.25(Oj2/D)min = 0.94, then calculations based on the constant molal rates would be seriously in error. When the average latent heats of vaporization at the bottom and top of the column differ appreciably, calculations based on the modified basis are to be preferred. 

The Kirchhoff equation as derived above riiould be applicable to both chemical and physical processes, but one highly important limitation must be borne in mind. For a chemical reaction there is no difficulty concerning (dAH/dT)p, i.e., the variation of AH with temperature, at constant pressure, since the reaction can be carried out at two or more temperatures and AH determined at the same pressure, e.g., 1 atm., in each case. For a phase change, such as fusion or vaporization, however, the ordinary latent heat of furion or vaporization (AH) is the value under equilibrium conditions, when a change of temperature is accompanied by a change of pressure. If equation (12.7) is to be applied to a phase change the AH s must refer to the same pressure at different temperatures these are consequently not the ordinary latent heats. If the variation of the equilibrium heat of fusion, vaporization or transition with temperature is required, equation (12.7) must be modified, as will be seen in 271. 

The heat transfer across the vapor layer and the temperature distribution in the solid, liquid, and vapor phases are shown in Fig. 13. In the subcooled impact, especially for a droplet of water, which has a larger latent heat, it has been reported that the thickness of the vapor layer can be very small and in some cases, the transient direct contact of the liquid and the solid surface may occur (Chen and Hsu, 1995). When the length scale of the vapor gap is comparable with the free path of the gas molecules, the kinetic slip treatment of the boundary condition needs to be undertaken to modify the continuum system. Consider the Knudsen number defined as the ratio of the average mean free path of the vapor to the thickness of the vapor layer ... 

---