Author: admin
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Shortcut Estimation of Saturation Properties
We found that the Clausius-Clapeyron equation leads to a simple, two-constant equation for the vapor pressure at low temperatures. What about higher temperatures? Certainly, the assumption of ideal gases used to derive the Clausius-Clapeyron equation is not valid as the vapor pressure becomes large at high temperature; therefore, we need to return to the Clapeyron…
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The Clausius-Clapeyron Equation
We can apply these concepts of equilibrium to obtain a remarkably simple equation for the vapor-pressure dependence on temperature at low pressures. As a “point of view of greatest simplicity,” the Clausius-Clapeyron equation is an extremely important example. Suppose we would like to find the slope of the vapor pressure curve, dPsat/dT. Since we are talking…
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Criteria for Phase Equilibrium
As an introduction to the constraint of phase equilibrium, let us consider an example. A piston/cylinder contains both propane liquid and vapor at –12°C. The piston is forced down a specified distance. Heat transfer is provided to maintain isothermal conditions. Both phases still remain. How much does the pressure increase? This is a trick question.…
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Practice Problems
P8.1. Develop an expression for the Gibbs energy departure function based on the Redlich-Kwong (1958) equation of state: (ANS. (G – Gig)/RT = –ln(1 – bρ) – aln(1 + bρ)/(bRT3/2) + Z – 1 – lnZ) P8.2. For certain fluids, the equation of state is given by Z = 1 – bρ/Tr. Develop an expression for the enthalpy departure function for fluids of this type. (ANS. –2bρ/Tr) P8.3. In…
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Important Equations
Eqns. 8.22–8.30 stand out in this chapter as the starting point for deriving the necessary departure function expressions for any equation of state. It is tempting to use spreadsheets or programs to add up the contributions from departure functions, reference states, and ideal gas temperature effects mindlessly, like a human computer. But keep in mind that…
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Summary
The study of departure functions often causes students great difficulty. That is understandable since it involves simultaneous application of physics and multivariable calculus. This may be the first instance in which students have applied these subjects in combination to such an extent. On the other hand, it is impressive to see what can be accomplished…
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Generalized Charts for the Enthalpy Departure
As in the case of the compressibility factor, it is often useful to have a visual idea of how generalized properties behave. Fig. 8.7 on page 324 is analogous to the compressibility factor charts from the previous chapter except that the formula for enthalpy is (H – Hig) = (H – Hig)0 + ω(H – Hig)1. Note that one primary influence in determining the liquid enthalpy…
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Implementation of Departure Formulas
The tasks that remain are to select a particular equation of state, take the appropriate derivatives, make the substitutions, develop compact expressions, and add up the change in properties. The good news is that many years of engineering research have yielded several preferred equations of state (see Appendix D) which can be applied generally to any…
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Pressure-Dependent Formulas
Occasionally, our equation of state is difficult to integrate to obtain departure functions using the formulas from Section 8.5. This is because the equation of state is more easily arranged and integrated in the form Z = f (T,P), such as the truncated virial EOS. For treating cases where an equation of state is written most simply as Z = f(T,ρ) such as…
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Summary of Density-Dependent Formulas
Formulas for departures at fixed T,P are listed below. These formulas are useful for an equation of state written most simply as Z = f(T,ρ) such as cubic EOSs. For treating cases where an equation of state is written most simply as Z = f (T,P) such as the truncated virial EOS, see Section 8.6. Useful formulas at fixed T,V include: