Specific enthalpy, calculation

An Excel macro is given in Appendix 7.2, and some results are shown in Figure 7.7. The macro is specific to the example reaction with v = - -l but can be generalized to other reactions. Components of the macro illustrate many of the previous examples. Specific heats and enthalpies are calculated analytically using the functional form of Equation (7.19) and the data in Tables 7.1 and 7.2. The main computational loop begins with the estimation of Kthermo using the methodology of Example (7.15). 

The specific enthalpies are calculated by integrating heat capacities and (for vapors) adding the heat of vaporization. 

Enthalpy is calculated by time-integration of the voltage and current assuming that the experiment is almost isobaric. The result is then divided by the mass of the sample and referenced to 298 K (25 °C) to yield the specific enthalpy. 

This book contains tables of the properties of water and steam from 0 to 800 and from 0 to 1000 bar which have been calculated using a set of equations accepted by the members of the Sixth International Conference on the Properties of Steam in 1967. Properties which are tabulated include the pressure, specific volume, density, specific enthalpy, specific heat of evaporation, specific entropy, specific isobaric heat capacity, dynamic viscosity, thermal conductivity, the Prandtl number, the ion-product of water, the dielectric constant, the isentropic exponent, the surface tension and Laplace coefficient. Also see items [43] and [70]. 

For non-polar components like hydrocarbons, the results are very satisfactory for calculations of vapor pressure, density, enthalpy, and specific, heat and reasonably close for viscosity and conductivity provided that is greater than 0.10. 

The specific enthalpy of a gas is calculated using the principle of corresponding states. The enthalpy of a gas mixture is equal to the sum of the ideal gas enthalpy and a correction term ... 

The lattice model that served as the basis for calculating ASj in the last section continues to characterize the Flory-Huggins theory in the development of an expression for AHj . Specifically, we are concerned with the change in enthalpy which occurs when one species is replaced by another in adjacent lattice sites. The situation can be represented in the notation of a chemical reaction ... 

Physical properties of the acid and its anhydride are summarized in Table 1. Other references for more data on specific physical properties of succinic acid are as follows solubiUty in water at 278.15—338.15 K (12) water-enhanced solubiUty in organic solvents (13) dissociation constants in water—acetone (10 vol %) at 30—60°C (14), water—methanol mixtures (10—50 vol %) at 25°C (15,16), water—dioxane mixtures (10—50 vol %) at 25°C (15), and water—dioxane—methanol mixtures at 25°C (17) nucleation and crystal growth (18—20) calculation of the enthalpy of formation using semiempitical methods (21) enthalpy of solution (22,23) and enthalpy of dilution (23). For succinic anhydride, the enthalpies of combustion and sublimation have been reported (24). 

Single-Effect Evaporators The heat requirements of a singleeffect continuous evaporator can be calculated by the usual methods of stoichiometry. If enthalpy data or specific heat and heat-of-solution data are not available, the heat requirement can be estimated as the sum of the heat needed to raise the feed from feed to product temperature and the heat required to evaporate the water. The latent heat of water is taken at the vapor-head pressure instead of at the product temperature in order to compensate partiaUv for any heat of solution. If sufficient vapor-pressure data are available for the solution, methods are available to calculate the true latent heat from the slope of the Diihriugliue [Othmer, Ind. Eng. Chem., 32, 841 (1940)]. 

Example 4 Calculation of the BP Method Use the BP method with the SRK eqiiation-of-state for K values and enthalpy departures to compute stage temperatures, interstage vapor and hqiiid flow rates and compositions, and rehoiler and condenser duties for the light-hydrocarhon distdlation-coliimn specifications shown in Fig. 13-51 with feed at 260 psia. The specifications are selected to obtain three products, a vapor distillate rich in Cri and C3, a vapor side-stream rich in n-C4, and a bottoms rich in n-C and n-Cg. 

Example 5 Calculation of the SR Method Use the SR method with the PR equation of state for K values and enthalpy departures. The oil was taken as n-dodecane. To compute stage temperatures and interstage vapor and hquid flow rates and compositions for ahsorher-column specifications shown in Fig. 13-52. Note that a secondary ahsorher oil is used in addition to the main ahsorher oil and that heat is withdrawn from the seventh theoretical stage. 

Calculations were made with the Grayson-Streed modification of the Chao-Seader method for K values and the Lee-Kesler method for enthalpy departures. Initial estimates for stage temperatures and flow rates were as follows, where numbers in parentheses are consistent with specifications ... 

What is the potential temperature rise by the desired reaction What is the rate of the temperature rise Enthalpy of desired reaction Specific heat Table of data Thermodynamic data Calculations estimations... 

In principle the heat required to bring the material up to its processing temperature may be calculated in the case of amorphous polymers by multiplying the mass of the material (IP) by the specific heat s) and the difference between the required melt temperature and ambient temperature (AT). In the case of crystalline polymers it is also necessary to add the product of mass times latent heat of melting of crystalline structures (L). Thus if the density of the material is D then the enthalpy or heat required ( ) to raise volume V to its processing temperature will be given by ... 

In calculations with humid air, when the pressure is not high (usually the atmosphetic pressure of 1 bar), water vapor and dry air can be handled as an ideal gas, as we have already done in Eqs. (4.76) and (4.78). For ideal gases the specific enthalpy is just a function of tempetatute ... 

Essentially, the analytical approach outlined above for the open circuit gas turbine plants is that used in modem computer codes. However, gas properties, taken from tables such as those of Keenan and Kaye [6], may be stored as data and then used directly in a cycle calculation. Enthalpy changes are then determined directly, rather than by mean specific heats over temperature ranges (and the estimation of n and n ), as outlined above. 

To use a thermodynamic graph, locate the fluid s initial state on the graph. (For a saturated fluid, this point lies either on the saturated liquid or on the saturated vapor curve, at a pressure py) Read the enthalpy hy volume v, and entropy from the graph. If thermodynamic tables are used, interpolate these values from the tables. Calculate the specific internal energy in the initial state , with Eq. (6.3.23). 

When thermodynamic tables are used, read the enthalpy hf, volume Vj, and entropy Sf of the saturated liquid at ambient pressure, po, interpolating if necessary. In the same way, read these values (hg, Vg, Sg) for the saturated vapor state at ambient pressure. Then use the following equation to calculate the specific internal energy... 

Properties for this new mixture can be calculated as above to obtain the specific enthalpy and specific volume. 

It should be born in mind, however, that the activation parameters calculated refer to the sum of several reactions, whose enthalpy and/or entropy changes may have different signs from those of the decrystalUzation proper. Specifically, the contribution to the activation parameters of the interactions that occur in the solvent system should be taken into account. Consider the energetics of association of the solvated ions with the AGU. We may employ the extra-thermodynamic quantities of transfer of single ions from aprotic to protic solvents as a model for the reaction under consideration. This use is appropriate because recent measurements (using solvatochromic indicators) have indicated that the polarity at the surface of cellulose is akin to that of aliphatic alcohols [99]. Single-ion enthalpies of transfer indicate that Li+ is more efficiently solvated by DMAc than by alcohols, hence by cellulose. That is, the equilibrium shown in Eq. 7 is endothermic ... 

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