Calculation of Enthalpy

Combining Equations 4.75 to 4.77 gives the difference between the enthalpy at pressure P and that at the standard pressure Po and is known as the enthalpy departure. 

Equation 4.78 defines the enthalpy departure from a reference state at temperature T and pressure Po  

The value of (8Z/dT)P can be obtained from an equation of state, such as the Peng-Robinson equation of state, and the integral in Equation 4.78 evaluated3. The enthalpy departure for the Peng-Robinson equation of state is given by3  

One problem remains. The reference enthalpy must be defined at temperature T and pressure P0. The reference state for enthalpy can be taken as an ideal gas. At zero pressure, fluids are in their ideal gaseous state and the enthalpy is independent of pressure. The ideal gas enthalpy can be calculated from ideal gas heat capacity data3  

Hpo = enthalpy at zero pressure and temperature T0, defined to be zero (kJ-kmol ) 

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This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. 

To know how linear equations can be used for calculation of enthalpies of gas-phase reactions... 

In the calculation of enthalpies it is necessary to define some standard reference slate at which the enthalpy is taken as zero. It is most convenient to take the melting point of the material constituting the vapour as the reference temperature, and the liquid state of the materia] as its standard state. 

There are two important relationships in thermochemistry which are very useful in the calculation of enthalpies of reactions. These are known as Hess s law and Kirchoff s equation. 

The overall enthalpy change is the same as that indicated earlier. An useful consequence of Hess s law is that thermochemical equations can be added and subtracted just like algebraic equations. This facilitates the calculation of enthalpy changes for reactions which cannot be studied experimentally. 

Rabuck, A. D., Scuseria, G. E., 1999, Assessment of Recently Developed Density Functionals for the Calculation of Enthalpies of Formation in Challenging Cases , Chem. Phys. Lett., 309, 450. 

Calculation of enthalpies of formation from the enthalpies of combustion of reactants and products This method is generally applicable for any combustible material for which the gross molecular formula is known. The enthalpies of combustion may be determined in a calorimeter using excess oxygen. Analysis of the combustion products may be appropriate. 

Results of calculations of enthalpies of formation using these methods, except for the enthalpies of combustion approach, are shown in Table 2.7. 

As an introduction to the technical aspects of the conference, the results of some studies conducted by the writer on two relevant subjects are presented below. The first commentary is concerned with the design of sour-water strippers and the effects of thermodynamic data on these designs the second commentary is concerned with the calculation of enthalpies of steam-containing mixtures, essential to the design of coal processing and related plants. 

In the calculations of enthalpies of formation of ionic compounds, the differences from the accepted experimental values (which are very accurate) are probably due to the essential simplicity of the model, rather than having any other significance. If large discrepancies are found between experimental and calculated quantities, this probably means that the model is in error and that the compounds have a considerable covalent character. 

Table 2 Data for calculation of enthalpies for sensible heat and the latent heat of vapourisation...

The calculation procedure consists of a determination of the air/fuel molar ratio that will result in a combustor outlet temperature of 2000F, followed by the calculation of enthalpy and entropy of flow streams at the various state points in the cycle. The net work output from the turbine is calculated by subtracting the compressor work requirements from the total turbine expansion work determined from the enthalpy balance. Irreversible entropy productions are calculated by a routine entropy balance around each process step. 

Our initial purpose in this chapter is to develop from the first and second laws the fundamental property relations which underlie the mathematical structure of thermodynamics. From these, we derive equations which allow calculation of enthalpy and entropy values from PVT and heat-capacity data. We then discuss the diagrams and tables by which both measured and calculated property values are presented for convenient use. Finally, we develop generalized correlations which allow estimates of property values to be made in the absence of complete experimental information. 

The generalized correlations for HR and SR, together with ideal-gas heat capacities, allow calculation of enthalpy and entropy values of gases at any temperature and pressure by Eqs. (6.45) and (6.46). For a change from state 1 ... 

Calculation of Enthalpy and Entropy Values for Other Temperatures ... 

The polynomial expressions for Cp in Table B.2 are based on experimental data for the listed compounds and provide a basis for accurate calculations of enthalpy changes. Several approximate methods follow for estimating heat capacities in the absence of tabulated formulas. 

The calculation of enthalpy changes for the heating or cooling of a mixture of known composition may often be simplified by calculating a heat capacity for the mixture in the following manner ... 

Sometimes the requirement of the most stable configuration is dropped, but this cannot be done if one also involves calculations of enthalpy changes. 

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