Category: Phase Equilibrium in a Pure Fluid

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…

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…

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…

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…

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…

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…

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…

To introduce the calculation of fugacity for liquids, consider Fig. 9.5. The shape of an isotherm below the critical temperature differs significantly from an ideal-gas isotherm. Such an isotherm is illustrated which begins in the vapor region at low pressure, intersects the phase boundary where vapor and liquid coexist, and then extends to higher pressure in…

The principle of calculation of the fugacity coefficient is the same by all methods—Eqn. 9.23 or 9.24 is evaluated. The methods look considerably different, usually because the P–V–T properties are summarized differently. All methods use the formula below and differ only in the manner the fugacity coefficient is evaluated. Equations of State Equations of state are the dominant method used in process…

We began the chapter by showing that Gibbs energy was equivalent in phases at equilibrium. Here we show that equilibrium may also be described by equivalence of fugacities. Since we may subtract Gig from both sides and divide by RT, giving Substituting Eqn. 9.22, which becomes Therefore, calculation of fugacity and equating in each phase becomes the preferred method of…