Enthalpy graphical determination

As this equation indicates, the operating lines for the trays below the feed are constructed using B as a pivot (Figure 5.11). This point has coordinates Xg and hg-Qs. and can be located graphically from the overall enthalpy balance, represented by a straight line through D and F. Point B is the intersection of this line with the vertical line through Xg, one of the specified variables. The feed composition Z and enthalpy Hp determine the coordinates of F. For a feed at its bubble point, F falls on the saturated liquid curve. 

The method of Ponchon and Savarit [2.61] is a graphical determination of the number of theoretical separation stages in counterflow columns. It is particularly applicable to binary mixtures in rectification processes. Exact results are obtained when the enthalpy-concentration diagram of Pon-... 

Fig. 6.2. Graphical Determination of Partial Molar Enthalpies of Mixing of Cadmium and Tin.

Depicting ln(X ) for a given reaction in relation to (1/T), the slope of the curve will at any point be —ArHf,/R. A graph of In(A o) in relation to (1/T) shows almost rectilinear curves since the reaction enthalpy for many reactions only varies slightly with temperature. Thus, this form of illustration is useful for a graphical determination of reaction enthalpy based on test data. 

EXAMPLE 6.16 Graphically determine values for the partial molar enthalpies of sulfuric acid and water in an... 

These equations are now employed in the determination of the required height of a cooling tower for a given duty. The method consists of the graphical evaluation of the relation between the enthalpy of the body of gas and the enthalpy of the gas at the interface with the liquid. The required height of the tower is then obtained by integration of equation 13.49. 

Worked Example 4.15 The isomerization of 1-butene (X) to form frans-2-butene (XI). The equilibrium constants of reaction are given below. Determine the enthalpy of reaction AH using a suitable graphical method. 

Extraction calculations involving more than three components cannot be done graphically but must be done by numerical solution of equations representing the phase equilibria and material balances over all the stages. Since extraction processes usually are adiabatic and nearly isothermal, enthalpy balances need not be made. The solution of the resulting set of equations and of the prior determination of the parameters of activity coefficient correlations requires computer implementation. Once such programs have been developed, they also may be advantageous for ternary extractions,... 

The determination of the association constant K values can be done either graphically or numerically (Kertes and Gutmann, 1976). The K values can be used to estimate thermodynamic quantities such as AG°, AH° and AS0. The interactions of polar substances, such as methanol, ethanol and acetone, with Aerosol OT in toluene systems were examined (Kon-no, 1993). The negative AG° value was found in the decreased order methanol > ethanol > acetone and the contribution to AG° was AH° > TAS°. This result indicates that the solubilization of three solutes with Aerosol OT micelle is an enthalpy driven process. 

The amount of energy that the steam turbine extracts from the steam depends on the enthalpy drop across the machine. The enthalpy of the steam is a function of its temperature and pressure. One can use a Mollier diagram as a graphic tool to determine the amount of energy available under a particular set of conditions. If in Figure 2.131 the inlet conditions correspond to point and the outlet conditions to point P2, a line drawn between these two points is called the "expansion line" and represents the operation of the turbine as it is extracting energy from the steam. In an ideal turbine, the steam would expand at a constant entropy (isentropically) and the condition of the exhaust steam, from an ideal machine (which has no losses), would correspond to point 3. 

The enthalpy measurements of Smith (3) in the range 298 to 1190 K were smoothed graphically and used to determine C. A... 

Each point on the saturated liquid curve is associated with a point on the saturated vapor curve at equilibrium with it. The equilibrium vapor and liquid compositions may be obtained from Y-X or Y-X diagrams. Saturated vapor and liquid points on the H-X diagram at equilibrium with each other are joined by straight lines called tie lines. The single-stage graphical representation described in Section 5.3.1 is an illustration of a tie line. If, for instance, X is known, L can be determined as a point on the saturated liquid curve with composition coordinate X. Point V must lie on the other end of the tie line on the saturated vapor curve. Point F can then be determined either from information on the relative rates of feed, liquid, and vapor or from its composition or enthalpy. 

For the case where the total flow rates Vj and Lj vary throughout each section of the column, these flow rates may be determined by solving the enthalpy balances simultaneously with the above set of equations. For binary mixtures, the desired solution may be found by use of either graphical methods (Refs. 10, 13) or the numerical methods proposed in subsequent chapters for the solution of problems involving the separation of multicomponent mixtures. 

The entropy at 298 K was determined from the graphical integration of the heat capacity data. The entropy below 50 K was obtained by extrapolation using Debye and Einstein functions, which were found to adequately represent the measured heat capacity data. The calculated entropy was (50.33 0.33) J-K -moP it is assumed that the error is Ict. From this value and an earlier value for the enthalpy of formation, [44KEL] determined a Gibbs energy of formation of - 1021.7 kJ-moP. This latter value is considerably lower than the value recommended in this review. 

For multicomponent mixtures, graphical representations of properties, as presented in Chapter 3, cannot be used to determine equilibrium-stage requirements. Analytical computational procedures must be applied with thermodynamic properties represented preferably by algebraic equations. Because mixture properties depend on temperature, pressure, and phase composition(s), these equations tend to be complex. Nevertheless the equations presented in this chapter are widely used for computing phase equilibrium ratios (K-values and distribution coefficients), enthalpies, and densities of mixtures over wide ranges of conditions. These equations require various pure species constants. These are tabulated for 176 compounds in Appendix I. By necessity, the thermodynamic treatment presented here is condensed. The reader can refer to Perry and Chilton as well as to other indicated sources for fundamental classical thermodynamic background not included here. 

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