Author: admin
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Binary VLE Using Raoult’s Law
For a small class of mixtures where the components have very similar molecular functionality and molecular size, the bubble-pressure line is found to be a linear function of composition as shown in Figs. 10.2 and 10.3. As was noted in Section 10.1, the T-x-y and P-x-y diagram shapes are related qualitatively by inverting one of the diagrams. Because the bubble pressure is a…
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Vapor-Liquid Equilibrium (VLE) Calculations
Classes of VLE Calculations Depending on the information provided, one may perform one of several types of vapor-liquid equilibrium (VLE) calculations to model the vapor-liquid partitioning. These are: bubble-point pressure (BP), dew-point pressure (DP), bubble-point temperature (BT), dew-point temperature (DT), and isothermal flash (FL) and adiabatic flash (FA). The specifications of the information required and the information to be computed are tabulated below in Table 10.1. Also shown…
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Introduction to Phase Diagrams
Before we delve into the details of calculating phase equilibria, let us introduce elementary concepts of common vapor-liquid phase diagrams. For a pure fluid, the Gibbs phase rule shows vapor-liquid equilibrium occurs with only one degree of freedom, F = C – P + 2 = 1 – 2 + 2 = 1. At one atmosphere pressure, vapor-liquid equilibria will occur at only one…
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Homework Problems
9.1. The heat of fusion for the ice-water phase transition is 335 kJ/kg at 0°C and 1 bar. The density of water is 1g/cm3 at these conditions and that of ice is 0.915 g/cm3. Develop an expression for the change of the melting temperature of ice as a function of pressure. Quantitatively explain why ice skates slide…
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Practice Problems
P9.1. Carbon dioxide (CP = 38 J/mol-K) at 1.5 MPa and 25°C is expanded to 0.1 MPa through a throttle valve. Determine the temperature of the expanded gas. Work the problem as follows: a. Assuming the ideal gas law (ANS. 298 K) b. Using the Peng-Robinson equation (ANS. 278 K, sat L + V) c. Using a CO2 chart, noting that…
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Summary
We began this chapter by introducing the need for Gibbs energy to calculate phase equilibria in pure fluids because it is a natural function of temperature and pressure. We also introduced fugacity, which is a convenient property to use instead of Gibbs energy because it resembles the vapor pressure more closely. We also showed that…
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Temperature Effects on G and f
The effect of temperature at fixed pressure is The Gibbs energy change with temperature is then dependent on entropy. Gibbs energy will decrease with increasing temperature. Since the entropy of a vapor is higher than the entropy of a liquid, the Gibbs energy will change more rapidly with temperature for vapor. Since the Gibbs energy…
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Stable Roots and Saturation Conditions
When multiple real roots exist, the fugacity is used to determine which root is stable as explained in Section 9.10. However, often we are seeking a value of a state property and we are unable to find a stable root with the target value. This section explains how we handle that situation. We use entropy for…
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Saturation Conditions from an Equation of State
The only thermodynamic specification that is required for determining the saturation temperature or pressure is that the Gibbs energies (or fugacities) of the vapor and liquid be equal. This involves finding the pressure or temperature where the vapor and liquid fugacities are equal. The interesting part of the problem comes in computing the saturation condition by…
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Calculation of Fugacity (Solids)
Fugacities of solids are calculated using the Poynting method, with the exception that the volume in the Poynting correction is the volume of the solid phase. Poynting method for solids. Any of the methods for vapors may be used for calculation of ϕsat. Psat is obtained from thermodynamic tables. Equations of state are generally not applicable for…