Calculation of specific enthalpy

Tabulated values of enthalpy are available only for the more common materials. In the absence of published data the following expressions can be used to estimate the specific enthalpy (enthalpy per unit mass). 

Cp = specific heat capacity of the material, constant pressure, 

If a phase transition takes place between the specified and datum temperatures, the latent heat of the phase transition is added to the sensible-heat change calculated by equation 3.11. The sensible-heat calculation is then split into two parts  

Cpj = specific heat capacity first phase, below Tp, 

CP2 = specific heat capacity second phase, above Tp. 

---

Since for steam turbine operation we may assume Cp > 2000 J/(kg K) and s - Sg < 2000 J/(kg K), squared and higher terms in (16.66) will contribute relatively little to the final figure, and may be neglected for the purpose of estimating the effect of the error in specific heat on the calculation of specific enthalpy. Assuming the error in average specific heat is fractional, we may expand using the binomial expansion ... 

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). 

There are two ways of calculating the specific enthalpy of the vapour at its boiling point. 

Calculate the specific enthalpy of water at a pressure of 1 bar and temperature of 200 °C. Check your value using steam tables. The specific heat capacity of water can be calculated from the equation ... 

Muller (1959) and co-workers have made many interesting and important studies of heat effects during the mechanical stretching and relaxing of polymeric fibers. However, Dole (1959) in reviewing calculations of the enthalpy differences between drawn and undrawn fibers and annealed samples as computed from specific heat-temperature data could find no differences that could not be explained on the basis of the extent of crystallinity of the samples. 

The specific internal energy of helium at 300 K and 1 atm is 3800 J/mol, and the specific molar volume at the same temperature and pressure is 24.63 L/mol. Calculate the specific enthalpy of helium at this temperature and pressure, and the rate at which enthalpy is transported by a stream of helium at 300 K and 1 atm with a molar flow rate of 250 kmol/h. 

What would you need to know to calculate the specific enthalpy of this fluid ... 

Five hundred kilograms per hour of steam drives a turbine. The steam enters the turbine at 44 atm and 450 C at a linear velocity of 60 m/s and leaves at a point 5 m below the turbine inlet at atmospheric pressure and a velocity of 360 m/s. The turbine delivers shaft work at a rate of 70 kW, and the heat loss from the turbine is estimated to be 10 kcal/h. Calculate the specific enthalpy change associated with the process. 

A gas mixture contains one-third methane by volume (recall what that means in terms of moIe%) and the balance oxygen at 350 C and 3.0 bar. Calculate the specific enthalpy of this stream in kJ/kg (not per kmoi) relative to the pure components at 25°C and 1 atm. State clearly all assumptions. 

A sulfuric acid solution is labeled 8N (where IN = 1 g-equivalent /L, and 1 mol of H2SO4 contains two g-equivalents). The specific gravity of the solution is 1.230, and its heat capacity is 3.00 J/(g- C). Calculate the specific enthalpy of this solution (in kJ/mol H2SO4) at 60 C relative to pure H2O and an infinitely dilute solution at 25 C. 

In the example, we would first calculate the specific enthalpy of the entering propane (Hi) as follows ... 

The calculation of an adiabatic flame temperature follows the general procedure outlined in Section 9.5b. Unknown stream flow rates are lirst determined by material balances. Reference conditions are chosen, specific enthalpies of feed components are calculated, and specific enthalpies of product components are expressed in terms of the product temperature, Finally, AH(Tiii) for the process is evaluated and substituted into the energy balance equation (Aw = 0), which is solved for... 

A convenient way to represent enthalpy data for binary solutions is via an enthalpy-concentration diagram. Enthalpy-concentration diagrams (H-x) are plots of specific enthalpy versus concentration (usually weight or mole fraction) with temperature as a parameter. Figure 4.21 illustrates one such plot. If available, such charts are useful in making combined material and energy balances calculations in distillation, crystallization, and all sorts of mixing and separation problems. You will find a few examples of enthalpy-concentration charts in Appendix I. 

This approximate two state model of water with bonded OH (which may have an angular partition around 6 = o) and "free" OH is basis for calculations of heat enthalpies, heat of vaporization, specific heat, surface energy, density and T-dependences under... 

Thus 4>bs will be less than value calculated for 0D, and take the value of specific enthalpy from the same row. This will be Hb,. 

Standard thermodynamic formalism for the total differential of specific enthalpy in terms of its natural variables (i.e., via Legendre transformation, see equations 29-20 and 29-24b) allows one to calculate the pressure coefQdent of specific enthalpy via a Maxwell relation and the definition of the coefficient of thermal expansion, a. 

In practice, pure-component molar enthalpies are employed to approximate A/7rx. This approximation is exact for ideal solutions only, when partial molar properties reduce to pure-component molar properties. In general, one accounts for more than the making and breaking of chemical bonds in (3-35). Nonidealities such as heats of solution and ionic interactions are also accounted for when partial molar enthalpies are employed. Now, the first law of thermodynamics for open systems, which contains the total differential of specific enthalpy, is written in a form that allows one to calculate temperature profiles in a tubular reactor ... 

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

---