Latent heat water heating curve

Figure 28 shows the key features of the humidity chart. The chart consists of the following four parameters plotted as ordinates against temperature on the abscissas (1) Humidity H, as pounds of water per pound of dry air, for air of various relative humidities (2) Specific volume, as cubic feet of dry air per pound of dry air (3) Saturated volume in units of cubic feet of saturated mixture per pound of dry air and (4) latent heat of vaporization (r) in units of Btu per pound of water vaporized. The chart also shows plotted hiunid heat (s) as abscissa versus the humidity (H) as ordinates, and adiabatic humidification curves (i.e., humidity versus temperature). Figure 28 represents mixtures of dry air and water vapor, whereby the total pressure of the mixture is taken as normal barometric. Defining the actual pressure of the water vapor in the mixture as p (in units of mm of mercury), the pressure of the dry air is simply 760 - p. The molal ratio of water vapor to air is p/(760-p), and hence the mass ratio is ... 

The specific volumes and the latent heats are generally quite different from the three changes of state, and therefore the slopes of the three curves at the triple point are also different. The difference in the slopes of the tangents of the solid-vapour (hoar frost line), and the liquid-vapour (steam line) curves of water (Fig. 39) is... 

Comprehensive tables of vapor-pressure data of common liquids, such as water, common refrigerants, and others, may be found in Refs. [2,3]. For most liquids, the vapor-pressure data are obtained at a few discrete temperatures, and it might frequently be necessary to interpolate between or extrapolate beyond these measurement points. At a constant pressure, the Clausius-Clapeyron equation relates the slope of the vapor pressure-temperature curve to the latent heat of vaporization through the relation... 

It is worthwhile pointing out here that, although the adiabatic saturation curve equation does not reveal anything of the enthalpy-humidity path of either the liquid phase or gas phase at various points in the contacting device (except for the air-water vapor system), each point within the system must conform with the wet bulb relation, which requires that the heat transferred be exactly consumed as latent heat of vaporization of the mass of liquid evaporated. The identity of hc/K with CpY was first found empirically by Lewis and hence is called the Lewis relation. The treatment given here on the wet bulb temperature applies only in the limit of very mild drying conditions when the vapor flux becomes directly... 

Once the drying rate curve and the residence time are known, the above equations (Equations 41.7 through 41.10) can be solved numerically to determine the changes in air temperature (7 ), air humidity (F), wood me (X), and wood temperature (T ). In Equation 41.9, A is the latent heat of water vaporization and, in Equation 41.10, AT is the temperature difference between the hot air and the solid material. The mass flow rate of the oven dry wood and that of the dry air are represented by symbols M and G, respectively. The moisture evaporation rate in one element is represented by R, and the heat transfer rate in the element is Q. 

Dissolution of the HCl in water sets free a large amount of heat of absorption (approximately as high as the latent heat of evaporation of water). Hence, the liquid in the absorber reaches boiling temperature and, in turn, some water is evaporated by the absorption of HCl. Hence, the conditions in the absorber are quite similar to those in a distillation column. The equilibrium curve of a boiling HCI/H2O liquid is shown in the McCabe-Thiele diagram of Fig. 11.1-6. The presence of the inert gases only reduces the effective pressine of the HCI/H2O system. 

Figure 7 shows the same corrections for a two-phase flow with a water/air mass flow ratio of 4.75% at 3.9m/s. The top curve corresponds to the preliminary results. Like the singlephase flow, as the heater input increases steady state temperature rises, however, the tenq)erature is lower for the two-phase flow. This augmentation of heat transfer is attributed to latent heat of evaporation of water droplets within the boundary layer. As the water/air mass flow ratio increases, the steady state temperature decreases for the same heater input... 

Equation 1.41 represents the adiabatic saturation curve on the psychrometric chart, which passes through the points (Ibs. Tbs) on the 100% saturation curve (ilf = 1) and B Y n, Tin), the initial condition. Since the humid heat contains the term lb, the curve is not straight but is curved slightly concave upward. Knowing the adiabatic saturation temperature and the actual gas temperature, the actual gas humidity can be easily obtained as the absolute humidity from the saturation locus. Equation 1.40 indicates that the sensible heat given up by the gas in cooling equals the latent heat required to evaporate the added vapor. It is important to note that, since Equation 1.41 is derived from the overall mass and energy balances between the initial gas conditions and the adiabatic saturation conditions, it is applicable only at these points and may not describe the path followed by the gas as it becomes saturated. A family of these adiabatic saturation curves for the air-water system are contained in the psychrometric charts [10]. 

Equations (3.72) to (3.74) are solved simultaneously by trial with the vapor-pressure curve for water, which relates and and the latent-heat data. It is easiest to > .. t- which is checked when q, from Eqs. (3.72) and (3.73) agree. 

Interpolation beriveen data For such common liquids as water, many refrigerants, and others, the vapor-pressure-temperature curve has been established at many points. For most liquids, however, only relatively few data are available, so that it is necessary frequently to interpolate between, or extrapolate beyond, the measurements. The curve on arithmetic coordinates (Fig. 7.1) is very inconvenient for this because of the curvature, and some method of linearizing the curve is needed. Most of the common methods stem from the Clausius-Clapeyron equation, which relates the slope of the vapor-pressure curve to the latent heat of vaporization... 

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