Internal energy and enthalpy

Clearly, Aid is equal to the heat transferred in a constant pressure process. Often, because biochemical reactions normally occur in liquids or solids rather than in gases, volume changes are small and enthalpy and internal energy are often essentially equal. 

For an ideal gas for which PV = RT/M, with representing the molecular weight, the enthalpy and internal energy are functions only of temperature and Equation 2-119 becomes... 

If the temperature of the inlet stream is taken as the datum temperature for enthalpy and internal energy calculations,... 

Before proceeding further, we will take a closer look at the significance of enthalpy and internal energy, because these cannot be measured directly but are determined indirectly by measuring other properties such as temperature and pressure. 

This relationship, of course, will hold for a shock wave when q is set equal to zero. The Hugoniot equation is also written in terms of the enthalpy and internal energy changes. The expression with internal energies is particularly useful in the actual solution for the detonation velocity tq. If a total enthalpy (sensible plus chemical) in unit mass terms is defined such that... 

The enthalpies and internal energies of steam and water also converge at the critical point. Tlie heat capacity at constant pressure. C,. is defined as the derivative of enthalpy with respect to temperature. The value of Cr, becomes very large in the vicinity of the critical point. The variation is much smaller for tlie heat capacity at constant volume, C,.. 

For liquids not near the critical point, the volume itself is small, as are both ft and k. Thus at most conditions pressure has little effect on the entropy, enthalpy, and internal energy of liquids. For an incompressiblefluid (Sec. 3.1), an idealization useful in fluid mechanics, both ft and k are zero. In this case both (dS/dP)T and (BU/dP)T are zero, and the entropy and internal energy are independent of P. However, the enthalpy of an Incompressible fluid is a function of P, as is evident from Eq. (6.25). 

What is a state function Enthalpy and internal energy are state functions as a direct consequence of the first law of thermodynamics. Why is this so ... 

In Chapter 7, we dealt only with processes involving species for which specific enthalpies and internal energies at specified conditions could be found in tables. Unfortunately, you cannot count on finding such data for every species with which you work. This chapter presents procedures for evaluating AH or A(/ when tables of H and U are not available for all process species. Once these calculations have been performed, the energy balance may be written and solved as before. 

Determine a heat of reaction from heats of other reactions using Hess s law. Determine standard enthalpies and internal energies of reaction from known standard heats of formation and heats of combustion. 

However, in high-pressure processes the second term on the right-hand side of Eq. (4.7) cannot necessarily be neglected, but must be evaluated from experimental data. Consult the references at the end of the chapter for details. One property of ideal gases that should be noted is that their enthalpies and internal energies are functions of temperature only and are not influenced by changes in pressure or specific volume. 

Calculate enthalpy (and internal energy) changes (excluding phase changes) from heat capacity equations, graphs and charts, tables, and computer data bases given the initial and final states of the material. 

In chemical thermodynamics, we define the zero of the enthalpy and internal energy as that of the elements as they exist in their stable forms at 298K and 1 atm pressure. Thus the enthalpies// of Xc(g), O2(g) and C(diamond) are all zero, as are those of H2 and Cl2 in the reaction... 

The Gibbs free energy of activation and Gibbs free energy of reaction are determined as with the enthalpy and internal energy discussed previously. 

The fact that the volume of the liquid is able to change has led to a temperature differential framed exclusively in terms of enthalpies. This is in contrast to the situation with the gas reactor, where the reaction volume was fixed, and we dealt with both enthalpies and internal energies. 

For the special case of the ideal gas, the enthalpy and internal energy of the fluid are functions only of temperature. In this case the partial derivatives above become total derivatives, and... 

The enthalpy and internal energy of an ideal gas at a temperature 7t can be related to their values at Ti by integration of Eqs. 3.3-4 to obtain... 

See the Common Units and Values for Problems and Examples inside the back cover. Several problems in this section deal with perfect gases. It may be shown that for a perfect gas the enthalpy and internal energy depend on temperature alone. If a perfect gas has a constant heat capacity (which may be assumed in all the perfect-gas problems in this chapter), it is very convenient to choose an enthalpy datum that leads to h = CpT and u= CyT, where T is the absolute temperature these values may be used in the perfect-gas problems in this chapter. For Freon 12 problems, use App. A.2. For steam and COj problems, use any standard table of values. 

FUNCTIONS FOR THE CALCULATION OF ENTROPY, ENTHALPY, AND INTERNAL ENERGY FOR REAL FLUIDS USING EQUATIONS OF STATE AND SPECIFIC HEATS... 

Several recent publications from this laboratory on the calculation of thermodynamic properties of cryogenic fluids contain various relations for the determination of entropy, enthalpy, and internal energy. Considerable interest has been expressed about the derivation and application of these equations this interest generally results from the fact that standard texts on thermodynamics are, almost without exception, inadequate in the presentation of material on the calculation of thermodynamic properties. The purpose of this paper is to derive the functions necessary for the calculation of these properties. These derivations are intended to give the reader a better understanding of the methods of calculating thermodynamic properties and thus of the limitations of the tables so produced. 

Calculation of Entropy, Enthalpy, and Internal Energy for Real Fluids... 

In extending the isotherms of the path of integration shown in Fig. 1 so that AB approaches the zero-pressure isobar, it is clear that the representation of the P-V-T surface for the real gas must be valid to these low pressures. (The value of PF from the real-gas equation of state must approach RT as P approaches zero.) As a consequence, it now also becomes convenient to choose the reference state on the ideal gas surface. Since a reference point at zero pressure would result in infinite entropies at any finite pressure on the real or ideal gas surface, the standard reference state is usually chosen at 1 atm and To on the ideal gas surface this is equivalent to choosing the standard reference values of enthalpy and internal energy at zero pressure and To, since and C/° are functions of temperature alone for the ideal gas. 

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