Details

Phase Modeling Tools


Phase Modeling Tools

Applications to Gases
1. Aufl.

von: Michel Soustelle

139,99 €

Verlag: Wiley
Format: PDF
Veröffentl.: 05.08.2015
ISBN/EAN: 9781119178460
Sprache: englisch
Anzahl Seiten: 300

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Beschreibungen

<p>This book is part of a set of books which offers advanced students successive characterization tool phases, the study of all types of phase (liquid, gas and solid, pure or multi-component), process engineering, chemical and electrochemical equilibria, and the properties of surfaces and phases of small sizes. Macroscopic and microscopic models are in turn covered with a constant correlation between the two scales. Particular attention has been given to the rigor of mathematical developments.</p>
<p>PREFACE xiii</p> <p>NOTATIONS xvii</p> <p>SYMBOLS  xix</p> <p><b>CHAPTER 1. THERMODYNAMIC FUNCTIONS AND VARIABLES  1</b></p> <p>1.1. State variables and characteristic functions of a phase 2</p> <p>1.1.1. Intensive and extensive conjugate variables 2</p> <p>1.1.2. Variations in internal energy during a transformation 3</p> <p>1.1.3 Characteristic function associated with a canonical set of variables  5</p> <p>1.2. Partial molar parameters 7</p> <p>1.2.1. Definition 7</p> <p>1.2.2. Properties of partial molar variables 8</p> <p>1.3. Chemical potential and generalized chemical potentials 8</p> <p>1.3.1. Chemical potential and partial molar free enthalpy  8</p> <p>1.3.2. Definition of generalized chemical potential  9</p> <p>1.3.3. Variations in the chemical potential and generalized chemical potential with variables 10</p> <p>1.3.4. Gibbs–Duhem relation 10</p> <p>1.3.5. Generalized Helmholtz relations 11</p> <p>1.3.6. Chemical system associated with the general system 12</p> <p>1.4. The two modeling scales  14</p> <p><b>CHAPTER 2. MACROSCOPIC MODELING OF A PHASE 15</b></p> <p>2.1. Thermodynamic coefficients and characteristic matrices 15</p> <p>2.1.1. Thermodynamic coefficients and characteristic matrix associated with the internal energy 15</p> <p>2.1.2. Symmetry of the characteristic matrix  17</p> <p>2.1.3. The thermodynamic coefficients needed and required to thermodynamically define the phase  17</p> <p>2.1.4. Choosing other variables: thermodynamic coefficients and characteristic matrix associated with a characteristic function 19</p> <p>2.1.5. Change in variable from one characteristic matrix to another  22</p> <p>2.1.6. Relations between thermodynamic coefficients and secondary derivatives of the characteristic function 26</p> <p>2.1.7. Examples of thermodynamic coefficients: calorimetric coefficients 27</p> <p>2.2. Partial molar variables and thermodynamic coefficients 27</p> <p>2.3. Common variables and thermodynamic coefficients  28</p> <p>2.3.1. State equation  29</p> <p>2.3.2. Expansion coefficients 30</p> <p>2.3.3. Molar heat capacities  32</p> <p>2.3.4. Young’s Modulus  34</p> <p>2.3.5. Electric permittivity  34</p> <p>2.3.6. Volumic and area densities of electric charge 34</p> <p>2.4. Thermodynamic charts: justification of different types  35</p> <p>2.4.1. Representation of a variable as a function of its conjugate 35</p> <p>2.4.2. Representation of a characteristic function as a function of one of its natural variables 38</p> <p>2.5. Stability of phases  39</p> <p>2.5.1. Case of ensemble E0 of extensive variables 40</p> <p>2.5.2. Coefficients associated with ensemble En  43</p> <p>2.5.3. Case of other ensembles of variables  44</p> <p>2.5.4. Conclusion: stability conditions of a phase in terms of thermodynamic coefficients  46</p> <p>2.5.5. Example – applying stability conditions  46</p> <p>2.6. Consistency of thermodynamic data 48</p> <p>2.7. Conclusion on the macroscopic modeling of phases  49</p> <p><b>CHAPTER 3. MULTI-COMPOUND PHASES – SOLUTIONS  51</b></p> <p>3.1. Variables attached to solutions 51</p> <p>3.1.1. Characterizing a solution  52</p> <p>3.1.2. Composition of a solution 53</p> <p>3.1.3. Peculiar variables and mixing variables 54</p> <p>3.2. Recap of ideal solutions 57</p> <p>3.2.1. Thermodynamic definition 57</p> <p>3.2.2. Molar Gibbs energy of mixing of an ideal solution  57</p> <p>3.2.3. Molar enthalpy of mixing of the ideal solution 57</p> <p>3.2.4. Molar entropy of mixing of the ideal solution  58</p> <p>3.2.5. Molar volume of mixing  58</p> <p>3.2.6. Molar heat capacity of ideal solution: Kopp’s law 58</p> <p>3.3. Characterization imperfection of a real solution 59</p> <p>3.3.1. Lewis activity coefficients 60</p> <p>3.3.2. Characterizing the imperfection of a real solution by the excess Gibbs energy  71</p> <p>3.3.3. Other ways to measure the imperfection of a solution 74</p> <p>3.4. Activity of a component in any solution: Raoult’s and Henry’s laws  76</p> <p>3.5. Ionic solutions 77</p> <p>3.5.1. Chemical potential of an ion  78</p> <p>3.5.2. Relation between the activities of ions and the overall activity of solutes  80</p> <p>3.5.3. Mean concentration and mean ionic activity coefficient 80</p> <p>3.5.4. Obtaining the activity coefficient of an individual ion 82</p> <p>3.5.5. Ionic strength 82</p> <p>3.6. Curves of molar variables as a function of the composition in binary systems of a solution with two components  83</p> <p><b>CHAPTER 4. STATISTICS OF OBJECT COLLECTIONS  87</b></p> <p>4.1. The need to statistically process a system  87</p> <p>4.1.1. Collections, system description – Stirling’s approximation  87</p> <p>4.1.2. Statistical description hypothesis 88</p> <p>4.1.3. The Boltzmann principle  89</p> <p>4.2. Statistical effects of distinguishable non-quantum elements  89</p> <p>4.2.1. Distribution law 90</p> <p>4.2.2. Calculation of  91</p> <p>4.2.3. Determining coefficient  92</p> <p>4.2.4. Energy input to a system  95</p> <p>4.2.5. The Boltzmann principle for entropy  96</p> <p>4.3. The quantum description and space of phases 97</p> <p>4.3.1. Wave functions and energy levels  97</p> <p>4.3.2. Space of phases: discernibility of objects and states 98</p> <p>4.3.3. Localization and non-localization of objects  98</p> <p>4.4. Statistical effect of localized quantum objects 99</p> <p>4.5. Collections of non-localized quantum objects 100</p> <p>4.5.1. Eigen symmetrical and antisymmetric functions of non-localized objects  101</p> <p>4.5.2. Statistics of non-localized elements with symmetrical wave functions 103</p> <p>4.5.3. Statistics of non-localized elements with an asymmetric function  105</p> <p>4.5.4. Classical limiting case 107</p> <p>4.6. Systems composed of different particles without interactions 107</p> <p>4.7. Unicity of coefficient  108</p> <p>4.8. Determining coefficient in quantum statistics  110</p> <p><b>CHAPTER 5. CANONICAL ENSEMBLES AND THERMODYNAMIC FUNCTIONS 113</b></p> <p>5.1. An ensemble 113</p> <p>5.2. Canonical ensemble 114</p> <p>5.2.1. Description of a canonical ensemble 114</p> <p>5.2.2. Law of distribution in a canonical ensemble  115</p> <p>5.2.3. Canonical partition function  116</p> <p>5.3. Molecular partition functions and canonical partition functions 117</p> <p>5.3.1. Canonical partition functions for ensembles of discernable molecules  117</p> <p>5.3.2. Canonical partition functions of indiscernible molecules  118</p> <p>5.4. Thermodynamic functions and the canonical partition function 120</p> <p>5.4.1. Expression of internal energy 120</p> <p>5.4.2. Entropy and canonical partition functions 121</p> <p>5.4.3. Expressing other thermodynamic functions and thermodynamic coefficients in the canonical ensemble 123</p> <p>5.5. Absolute activity of a constituent 125</p> <p>5.6. Other ensembles of systems and associated characteristic functions  127</p> <p><b>CHAPTER 6. MOLECULAR PARTITION FUNCTIONS 131</b></p> <p>6.1. Definition of the molecular partition function  131</p> <p>6.2. Decomposition of the molecular partition function into partial partition functions 131</p> <p>6.3. Energy level and thermal agitation 133</p> <p>6.4. Translational partition functions  134</p> <p>6.4.1. Translational partition function with the only constraint being the recipient 135</p> <p>6.4.2. Translational partition function with the constraint being a potential centered and the container walls  137</p> <p>6.5. Maxwell distribution laws  139</p> <p>6.5.1. Distribution of ideal gas molecules in volume 139</p> <p>6.5.2. Distribution of ideal gas molecules in velocity 140</p> <p>6.6. Internal partition functions 142</p> <p>6.6.1. Vibrational partition function 142</p> <p>6.6.2. Rotational partition function  144</p> <p>6.6.3. Nuclear partition function and correction of symmetry due to nuclear spin 146</p> <p>6.6.4. Electronic partition function  149</p> <p>6.7. Partition function of an ideal gas  149</p> <p>6.8. Average energy and equipartition of energy 150</p> <p>6.8.1. Mean translational energy 151</p> <p>6.8.2. Mean rotational energy 152</p> <p>6.8.3. Mean vibrational energy  152</p> <p>6.9. Translational partition function and quantum mechanics 153</p> <p>6.10. Interactions between species 155</p> <p>6.10.1. Interactions between charged particles 155</p> <p>6.10.2. Interaction energy between two neutral molecules  156</p> <p>6.11. Equilibrium constants and molecular partition functions 161</p> <p>6.11.1. Gaseous phase homogeneous equilibria  162</p> <p>6.11.2. Liquid phase homogeneous equilibria 164</p> <p>6.11.3. Solid phase homogenous equilibria 166</p> <p>6.12. Conclusion on the macroscopic modeling of phases 167</p> <p><b>CHAPTER 7. PURE REAL GASES 169</b></p> <p>7.1. The three states of the pure compound: critical point  169</p> <p>7.2. Standard state of a molecular substance  170</p> <p>7.3. Real gas – macroscopic description  171</p> <p>7.3.1. Pure gas diagram (P-V) 171</p> <p>7.3.2. “Cubic” state equations 172</p> <p>7.3.3. Other state equations  177</p> <p>7.3.4. The theorem of corresponding states and the generalized compressibility chart  180</p> <p>7.3.5. Molar Gibbs energy or chemical potential of a real gas 182</p> <p>7.3.6. Fugacity of a real gas  183</p> <p>7.3.7. Heat capacities of gases  186</p> <p>7.4. Microscopic description of a real gas 188</p> <p>7.4.1. Canonical partition function of a fluid  188</p> <p>7.4.2. Helmholtz energy and development of the virial 195</p> <p>7.4.3. Forms of the second coefficient of the virial  197</p> <p>7.4.4. Macroscopic state equations and microscopic description  202</p> <p>7.4.5. Chemical potential and fugacity of a real gas 203</p> <p>7.4.6. Conclusion on microscopic modeling of a real gas  204</p> <p>7.5. Microscopic approach of the heat capacity of gases  206</p> <p>7.5.1. Classical theorem from the equipartition of energy  207</p> <p>7.5.2. Quantum theorem of heat capacity at constant volume  208</p> <p><b>CHAPTER 8. GAS MIXTURES  213</b></p> <p>8.1. Macroscopic modeling of gas mixtures 213</p> <p>8.1.1. Perfect solutions of perfect gases 213</p> <p>8.1.2. Mixture of real gases  215</p> <p>8.2. Characterizing gas mixtures  217</p> <p>8.2.1. Method of the state equations of gas mixtures 218</p> <p>8.2.2. The Beattie–Bridgeman state equation 218</p> <p>8.2.3. Calculating the compressibility coefficient of a mixture 222</p> <p>8.2.4. Method using activity coefficients of solutions  225</p> <p>8.3. Determining activity coefficients of a solution from an equation of state  225</p> <p>8.3.1. Methodology 226</p> <p>8.3.2. Studying solutions using the PSRK method  227</p> <p>8.3.3. VTPR Model 230</p> <p>8.3.4. VGTPR Model 233</p> <p>APPENDICES 237</p> <p>APPENDIX 1 239</p> <p>APPENDIX 2 243</p> <p>APPENDIX 3 245</p> <p>APPENDIX 4 253</p> <p>APPENDIX 5 257</p> <p>BIBLIOGRAPHY 261</p> <p>INDEX 265</p>
<p><strong>Michel SOUSTELLE</strong> is a chemical engineer and Emeritus Professor at Ecole des Mines de Saint-Etienne in France. He taught chemical kinetics from postgraduate to Master degree level while also carrying out research in this topic.

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