CHEMICAL AVAILABILITY
F. CHEMICAL AVAILABILITY
Our discussion thus far has considered systems for which the dead state is in thermo–mechanical (TM) equilibrium. For instance, consider compressed dry air that is con- tained in a piston–cylinder assembly that is placed in an ambient under standard conditions. The air may be expanded to its dead state and, in the process, produce work. At the dead state Our discussion thus far has considered systems for which the dead state is in thermo–mechanical (TM) equilibrium. For instance, consider compressed dry air that is con- tained in a piston–cylinder assembly that is placed in an ambient under standard conditions. The air may be expanded to its dead state and, in the process, produce work. At the dead state
40% N 2 and 60% O 2 , while the ambient still contains dry air (consisting of 79% N 2 and 21%
O 2 ). Although thermo–mechanical equilibrium is achieved when the gas is fully expanded to restricted dead state conditions (thermo-mechanical equilibrium), mass transfer occurs when the constraint is removed, i.e., the composition within the cylinder changes irreversibly. Recall that chemical potential of species k is the same as Gibb´s function which depends upon species concentration. Thus, the difference in concentration between the gas in the system and air in the ambient leads to difference in Gibb´s function and hence irreversible mass transfer of spe-
cies k (Chapter 3). The ambient gains O 2 molecules, trying to alter its partial pressures in the environment. The overall composition of the combined isolated system (piston–cylinder and ambient) is not the same as it was before implying that the entropy of the isolated system must have increased. Therefore, even if a system exists in thermo–mechanical equilibrium, this does not assure a zero entropy increase when the constraints upon it are removed.
Similarly, consider a turbine in which compressed air is expanded to the dead state which exists at standard conditions. Upon discharge to the dead state, it exits the turbine with negligible kinetic energy and its state does not change, since the air exists in thermo–mechanical equilibrium with the ambient. On the other hand, if compressed nitrogen is expanded through the turbine, its state will change from pure nitrogen to an air–nitrogen mix- ture as it mixes with the ambient air. In this section we will discuss a methodology to deter- mine the optimum work in cases where thermo–mechanical equilibrium exists, but irreversible
mixing occurs. If somehow, the N 2 is released at pressure equal to ambient partial pressure of
N 2 , then there is no irreversible mixing and chemical equilibrium now exists in addition to TM equilibrium. We wish to derive relations for the optimum work when matter reaches thermo- mechanical-chemical (TMC) equilibrium. Before doing so, we will briefly describe semi- permeable membranes. These membranes are permeable to specific species only, e.g., if dirty water is filtered through a charcoal bed, the bed can be designed to be permeable mostly to water, but impermeable to any particulate matter that it carries. Similarly, semipermeable membranes can be designed to separate water (solvent) and salt (solute), and gas mixtures.
Parts
» COMPUTATIONAL MECHANICS and APPLIED ANALYSIS
» Explicit and Implicit Functions and Total Differentiation
» Exact (Perfect) and Inexact (Imperfect) Differentials
» Intermolecular Forces and Potential Energy
» Internal Energy, Temperature, Collision Number and Mean Free Path
» Vector or Cross Product r The area A due to a vector product
» First Law for a Closed System
» First Law For an Open System
» STATEMENTS OF THE SECOND LAW
» Cyclical Integral for a Reversible Heat Engine
» Irreversibility and Entropy of an Isolated System
» Degradation and Quality of Energy
» SINGLE–COMPONENT INCOMPRESSIBLE FLUIDS
» Evaluation of Entropy for a Control Volume
» Internally Reversible Work for an Open System
» MAXIMUM ENTROPY AND MINIMUM ENERGY
» Generalized Derivation for a Single Phase
» LaGrange Multiplier Method for Equilibrium
» Absolute and Relative Availability Under Interactions with Ambient
» Irreversibility or Lost Work
» Applications of the Availability Balance Equation
» Closed System (Non–Flow Systems)
» Heat Pumps and Refrigerators
» Work Producing and Consumption Devices
» Graphical Illustration of Lost, Isentropic, and Optimum Work
» Flow Processes or Heat Exchangers
» CLASSICAL RATIONALE FOR POSTULATORY APPROACH
» Generalized Legendre Transform
» Van der Waals (VW) Equation of State
» Other Two–Parameter Equations of State
» Compressibility Charts (Principle of Corresponding States)
» Boyle Temperature and Boyle Curves
» Three Parameter Equations of State
» Empirical Equations Of State
» State Equations for Liquids/Solids
» Internal Energy (du) Relation
» EXPERIMENTS TO MEASURE (u O – u)
» Vapor Pressure and the Clapeyron Equation
» Saturation Relations with Surface Tension Effects
» Temperature Change During Throttling
» Throttling in Closed Systems
» Procedure for Determining Thermodynamic Properties
» Euler and Gibbs–Duhem Equations
» Relationship Between Molal and Pure Properties
» Relations between Partial Molal and Pure Properties
» Mixing Rules for Equations of State
» Partial Molal Properties Using Mixture State Equations
» Ideal Solution and Raoult’s Law
» Completely Miscible Mixtures
» DEVIATIONS FROM RAOULT’S LAW
» Mathematical Criterion for Stability
» APPLICATION TO BOILING AND CONDENSATION
» Physical Processes and Stability
» Constant Temperature and Volume
» Equivalence Ratio, Stoichiometric Ratio
» Entropy, Gibbs Function, and Gibbs Function of Formation
» Entropy Generated During an Adiabatic Chemical Reaction
» MASS CONSERVATION AND MOLE BALANCE EQUATIONS
» Evaluation of Properties During an Irreversible Chemical Reaction
» Criteria in Terms of Chemical Force Potential
» Generalized Relation for the Chemical Potential
» Nonideal Mixtures and Solutions
» Gas, Liquid and Solid Mixtures
» Availability Balance Equation
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