Enthalpy of liquids

Enthalpies are referred to the ideal vapor. The enthalpy of the real vapor is found from zero-pressure heat capacities and from the virial equation of state for non-associated species or, for vapors containing highly dimerized vapors (e.g. organic acids), from the chemical theory of vapor imperfections, as discussed in Chapter 3. For pure components, liquid-phase enthalpies (relative to the ideal vapor) are found from differentiation of the zero-pressure standard-state fugacities these, in turn, are determined from vapor-pressure data, from vapor-phase corrections and liquid-phase densities. If good experimental data are used to determine the standard-state fugacity, the derivative gives enthalpies of liquids to nearly the same precision as that obtained with calorimetric data, and provides reliable heats of vaporization. 

Each fluid is described by a BWR equation of state whose coefficients are adjusted to obtain simultaneously the vapor pressure, enthalpies of liquid and gas as well as the compressibilities. The compressibility z of any fluid is calculated using the equation below ... 

FIG. 2-11 Enthalpy-concentration diagram for aqueous hydrogen chloride at 1 atm. Reference states enthalpy of liquid water at 0 C is zero enthalpy of pure saturated HCl vapor at 1 atm (—85.03 C) is 8000 kcal/moL NOTE It should he observed that the weight basis includes the vapor, which is particularly important in the two-phase region. Saturation values may be read at the ends of the tie lines. [Van Nuys, Trans. Am. Inst. Chem. Eng., 39, 663 (1943).]... 

The diagram in Fig. 11-101 presents enthalpy data for LiBr-water solutions. It is needed for the thermal calculation of the cycle. Enthalpies for water and water vapor can be determined from the table or properties of water. The data in Fig. 11-101 are apphcable to saturated or subcooled solutions and are based on a zero enthalpy of liquid water at 0°C and a zero enthalpy of solid LiBr at 25°C. Since... 

To accommodate the step-by-step, recycling and checking for convergences requires input of vapor pressure relationships (such as Wilson s, Renon s, etc.) through the previously determined constants, latent heat of vaporization data (equations) for each component (or enthalpy of liquid and vapor), specific heat data per component, and possibly special solubility or Henry s Law deviations when the system indicates. 

Equations for calculating enthalpy of liquid of each component as a function of temperature... 

HK = Heavy key component in volatile mixture h = Enthalpy of liquid mixture or pure compound at tray conditions of temperature and pressure, or specified point or condition, Btu/lb mol, or Btu/lb... 

Figure 3.3. Enthalpy-concentration diagram for aqueous ammonia. Reference states enthalpies of liquid water at 0°C and liquid ammonia at —77°C are zero. (Bosniakovic, Technische Thermodynamik, T. Steinkopff,... 

To calculate the enthalpy of liquid or gas at temperature T and pressure P, the enthalpy departure function (Equation 4.78) is evaluated from an equation of state2. The ideal gas enthalpy is calculated at temperature T from Equation 4.81. The enthalpy departure is then added to the ideal gas enthalpy to obtain the required enthalpy. Note that the enthalpy departure function calculated from Equation 4.78 will have a negative value. This is illustrated in Figure 4.9. The calculations are complex and usually carried out using physical property or simulation software packages. However, it is important to understand the basis of the calculations and their limitations. 

He — local enthalpy of liquid at given axial location... 

We have already illustrated equation 2.32 for a solution enthalpy (of liquid ethanol see section 2.5). We now apply it to another phase transition the vaporization of a pure substance. 

The pressure effect on the enthalpy of liquid ethanol can be estimated from equation 2.15, now written in terms of the coefficient of thermal expansion, a ... 

Fig. 15. The enthalpy of liquid water calculated from the Weres-Rice model (from Ref. 64>) Fig. 16. The entropy of liquid water calculated from the Weres-Rice model (from Ref. 84>) Fig. 17. The specific heat of liquid water calculated from the Weres-Rice model (from Ref. 64>)...

Figure 11.24. Enthalpy-composition diagram, showing the enthalpies of liquid and vapour...

It may be assumed that the enthalpies of liquid and vapour are linear functions of composition. Enthalpy and equilibrium data are provided. 

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