Residual enthalpy and entropy

Calculated values of the quantities (Hr)°/RTc, (HRy/RTc, (Sr)°/R, an (SRy/R are shown by plots of these quantities vs. Pr for various values of Tr i Figs. 6.6 through 6.13. These plots, together with Eqs. (6.56) and (6.57), alio estimation of the residual enthalpy and entropy on the basis of the three-paramet corresponding-states principle as developed by Pitzer (Sec. 3.6). 

The generalized methods developed in Sec. 3.6 for the compressibility factor and in Sec. 6.6 for the residual enthalpy and entropy of pure gases are appli... 

Residual enthalpy and entropy, 158, 159 Reverse osmosis. See Osmosis,... 

Equations for residual enthalpy and entropy may be developed from... 

The usefulness of the residual properties should now be clear the calculation of AH and AS reduces to the calculation of the residual enthalpy and entropy at the initial and final state. Notice that the only heat... 

Calculate the residual enthalpy and entropy at 220 K, 20 bar assuming the validity of the truncated virial equation. Is the assumption justified ... 

The importance of eqs. f and f 5.40 ) is that they relate residual enthalpy and entropy to the equation of state. In the above form, these equations are useful if the equation of state can be expressed as function of pressure and temperature. Cubic equations express pressure in terms of volume and temperature to calculate residual properties from such equations, eqs. and must be converted so that the independent variables are V and T. The mathematical manipulations are shown on next page. 

In the previous section we discussed the calculation of residual properties from cubic equations of state. The calculations are straightforward, though somewhat time consuming. A quicker alternative is to use generalized graphs. In Chapter 2 we discussed the Pitzer method for calculating the compressibility factor in terms of reduced temperature, reduced pressure, and acentric factor. Analogous equations can be obtained for the residual enthalpy and entropy. In this approach, the residual enthalpy, made dimensionless by the product RTc, is computed as... 

This calculation requires the residual enthalpy and entropy at the reference state. These are constant and only need to be evaluated once. If the system at the reference pressure and temperature exists in multiple phases, the reference phase must be specified as well. For the steam tables, for example, the reference state is the saturated liquid at the triple point. 

The calculation of properties requires the residual enthalpy and entropy. These are intermediate properties and maybe understood as corrections to the ideal-gas equations due to intermolecular interactions. If interactions could be turned off, the residual terms would drop off and all that is left then is the ideal-gas contribution. In contrast with the real ideal-gas state, which is reached by reducing pressure at constant temperature, this hypothetical ideal-gas state is reached, hypothetically of course, at constant temperature and pressure by turning off interactions. 

The residual Gibbs energy can be calculated from the residual enthalpy and entropy. Accordingly, all the methods developed for the residual enthalpy and entropy maybe used to calculate GF, and from eg. 

Therefore, the calculation of the fugacity coefficient by a cubic equation of state does not require much in terms of additional computations, since the required expressions for the residual enthalpy and entropy have been obtained already. In particular, the result for the Soave-Redlich-Kwong and the Peng-Robinson equation are... 

Problem 7.20 Use the program you wrote in Problem 7.IQ to construct a PH graph for propane using as reference state the saturated liquid at 350 K. You may do this as follows First, obtain the residual enthalpy of the saturated liquid at 350 K. Next, calculate P= , and the residual enthalpy and entropy of the saturated liquid and saturated vapor at various temperatures between To and 250 K. Using these residuals and the specified reference state, calculate the absolute enthalpy of the saturated phases. 

Use the compressibility factor to calculate the residual enthalpy and entropy according to the equations in Table... 

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