16: Thermodynamic Tools III
- Page ID
- 564
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Module Goal: To establish the mathematical framework for thermodynamics of phase equilibrium.
- Module Objective: To establish that there is an unique relationship between partial molar quantities in any mixture.
- 16.1: The Chemical Potentials
- This page covers chemical potential as a thermodynamic property linked to energy under constant pressure and temperature. Defined as the change in Gibbs free energy with substance addition, it indicates a system's work capacity. The concept ties back to J.W. Gibbs' work on energy increments from substance addition in a homogeneous mass.
- 16.2: The Thermodynamic Concept of Equilibrium
- This page discusses the concept of equilibrium, highlighting its various forms: thermal, mechanical, and thermodynamic. Thermal equilibrium is defined by equal temperatures, while mechanical equilibrium relates to equal pressures. For thermodynamic equilibrium, constant properties are essential. In vapor-liquid systems, equilibrium occurs when the chemical potential is the same in both phases, preventing net transfer.
- 16.3: Fugacity
- This page examines Gibbs energy in closed systems, emphasizing its relationship with pressure and temperature. It introduces fugacity as a critical concept extending beyond ideal gases, linking it to Gibbs energy changes and chemical potential. The fugacity coefficient reflects non-ideality, with values near unity signifying ideal behavior.
- 16.4: Expressions for Fugacity Calculation
- This page provides a comprehensive overview of fugacity calculation essential for equilibrium studies. It defines fugacity through chemical potential and utilizes Maxwell's Relationships to introduce the fugacity coefficient. The page presents integral expressions connecting fugacity coefficients to pressure, temperature, and volume, and extends the discussion to multicomponent mixtures with important equations.
- 16.5: Cubic EOS Fugacity Expressions
- This page covers the calculation of fugacity utilizing P-explicit cubic equations of state, specifically the Soave-Redlich-Kwong and Peng-Robinson EOS. It provides expressions for the fugacity coefficients of pure substances and mixtures, emphasizing the key parameters A, B, and the Z-factor without delving into detailed derivations. The discussion culminates in connecting fugacity to vapor-liquid equilibrium, indicating a segue into practical applications in later sections.
- 16.6: Action Item
- This page discusses chemical potential as the change in free energy with the addition of a substance, indicating its reactive tendency. It also explains fugacity as an adjusted pressure that represents non-ideal gas behavior. Both concepts are crucial for understanding phase equilibrium, as they help identify conditions under which solid, liquid, and gas phases can coexist stably.