{"product_id":"phase-modeling-tools-applications-to-gases-hardback-9781848218642","title":"Phase Modeling Tools; Applications to Gases (Hardback) 9781848218642","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003ePhase Modeling Tools\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eApplications to Gases\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eMichel Soustelle (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781848218642, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 4 August 2015\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e300 pages\u003cbr\u003e16.5 x 16.3 x 2.3 cm, 0.59 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eThis 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.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003ePREFACE xiii\u003c\/p\u003e \u003cp\u003eNOTATIONS xvii\u003c\/p\u003e \u003cp\u003eSYMBOLS  xix\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 1. THERMODYNAMIC FUNCTIONS AND VARIABLES  1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1. State variables and characteristic functions of a phase 2\u003c\/p\u003e \u003cp\u003e1.1.1. Intensive and extensive conjugate variables 2\u003c\/p\u003e \u003cp\u003e1.1.2. Variations in internal energy during a transformation 3\u003c\/p\u003e \u003cp\u003e1.1.3 Characteristic function associated with a canonical set of variables  5\u003c\/p\u003e \u003cp\u003e1.2. Partial molar parameters 7\u003c\/p\u003e \u003cp\u003e1.2.1. Definition 7\u003c\/p\u003e \u003cp\u003e1.2.2. Properties of partial molar variables 8\u003c\/p\u003e \u003cp\u003e1.3. Chemical potential and generalized chemical potentials 8\u003c\/p\u003e \u003cp\u003e1.3.1. Chemical potential and partial molar free enthalpy  8\u003c\/p\u003e \u003cp\u003e1.3.2. Definition of generalized chemical potential  9\u003c\/p\u003e \u003cp\u003e1.3.3. Variations in the chemical potential and generalized chemical potential with variables 10\u003c\/p\u003e \u003cp\u003e1.3.4. Gibbs–Duhem relation 10\u003c\/p\u003e \u003cp\u003e1.3.5. Generalized Helmholtz relations 11\u003c\/p\u003e \u003cp\u003e1.3.6. Chemical system associated with the general system 12\u003c\/p\u003e \u003cp\u003e1.4. The two modeling scales  14\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 2. MACROSCOPIC MODELING OF A PHASE 15\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1. Thermodynamic coefficients and characteristic matrices 15\u003c\/p\u003e \u003cp\u003e2.1.1. Thermodynamic coefficients and characteristic matrix associated with the internal energy 15\u003c\/p\u003e \u003cp\u003e2.1.2. Symmetry of the characteristic matrix  17\u003c\/p\u003e \u003cp\u003e2.1.3. The thermodynamic coefficients needed and required to thermodynamically define the phase  17\u003c\/p\u003e \u003cp\u003e2.1.4. Choosing other variables: thermodynamic coefficients and characteristic matrix associated with a characteristic function 19\u003c\/p\u003e \u003cp\u003e2.1.5. Change in variable from one characteristic matrix to another  22\u003c\/p\u003e \u003cp\u003e2.1.6. Relations between thermodynamic coefficients and secondary derivatives of the characteristic function 26\u003c\/p\u003e \u003cp\u003e2.1.7. Examples of thermodynamic coefficients: calorimetric coefficients 27\u003c\/p\u003e \u003cp\u003e2.2. Partial molar variables and thermodynamic coefficients 27\u003c\/p\u003e \u003cp\u003e2.3. Common variables and thermodynamic coefficients  28\u003c\/p\u003e \u003cp\u003e2.3.1. State equation  29\u003c\/p\u003e \u003cp\u003e2.3.2. Expansion coefficients 30\u003c\/p\u003e \u003cp\u003e2.3.3. Molar heat capacities  32\u003c\/p\u003e \u003cp\u003e2.3.4. Young’s Modulus  34\u003c\/p\u003e \u003cp\u003e2.3.5. Electric permittivity  34\u003c\/p\u003e \u003cp\u003e2.3.6. Volumic and area densities of electric charge 34\u003c\/p\u003e \u003cp\u003e2.4. Thermodynamic charts: justification of different types  35\u003c\/p\u003e \u003cp\u003e2.4.1. Representation of a variable as a function of its conjugate 35\u003c\/p\u003e \u003cp\u003e2.4.2. Representation of a characteristic function as a function of one of its natural variables 38\u003c\/p\u003e \u003cp\u003e2.5. Stability of phases  39\u003c\/p\u003e \u003cp\u003e2.5.1. Case of ensemble E0 of extensive variables 40\u003c\/p\u003e \u003cp\u003e2.5.2. Coefficients associated with ensemble En  43\u003c\/p\u003e \u003cp\u003e2.5.3. Case of other ensembles of variables  44\u003c\/p\u003e \u003cp\u003e2.5.4. Conclusion: stability conditions of a phase in terms of thermodynamic coefficients  46\u003c\/p\u003e \u003cp\u003e2.5.5. Example – applying stability conditions  46\u003c\/p\u003e \u003cp\u003e2.6. Consistency of thermodynamic data 48\u003c\/p\u003e \u003cp\u003e2.7. Conclusion on the macroscopic modeling of phases  49\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 3. MULTI-COMPOUND PHASES – SOLUTIONS  51\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1. Variables attached to solutions 51\u003c\/p\u003e \u003cp\u003e3.1.1. Characterizing a solution  52\u003c\/p\u003e \u003cp\u003e3.1.2. Composition of a solution 53\u003c\/p\u003e \u003cp\u003e3.1.3. Peculiar variables and mixing variables 54\u003c\/p\u003e \u003cp\u003e3.2. Recap of ideal solutions 57\u003c\/p\u003e \u003cp\u003e3.2.1. Thermodynamic definition 57\u003c\/p\u003e \u003cp\u003e3.2.2. Molar Gibbs energy of mixing of an ideal solution  57\u003c\/p\u003e \u003cp\u003e3.2.3. Molar enthalpy of mixing of the ideal solution 57\u003c\/p\u003e \u003cp\u003e3.2.4. Molar entropy of mixing of the ideal solution  58\u003c\/p\u003e \u003cp\u003e3.2.5. Molar volume of mixing  58\u003c\/p\u003e \u003cp\u003e3.2.6. Molar heat capacity of ideal solution: Kopp’s law 58\u003c\/p\u003e \u003cp\u003e3.3. Characterization imperfection of a real solution 59\u003c\/p\u003e \u003cp\u003e3.3.1. Lewis activity coefficients 60\u003c\/p\u003e \u003cp\u003e3.3.2. Characterizing the imperfection of a real solution by the excess Gibbs energy  71\u003c\/p\u003e \u003cp\u003e3.3.3. Other ways to measure the imperfection of a solution 74\u003c\/p\u003e \u003cp\u003e3.4. Activity of a component in any solution: Raoult’s and Henry’s laws  76\u003c\/p\u003e \u003cp\u003e3.5. Ionic solutions 77\u003c\/p\u003e \u003cp\u003e3.5.1. Chemical potential of an ion  78\u003c\/p\u003e \u003cp\u003e3.5.2. Relation between the activities of ions and the overall activity of solutes  80\u003c\/p\u003e \u003cp\u003e3.5.3. Mean concentration and mean ionic activity coefficient 80\u003c\/p\u003e \u003cp\u003e3.5.4. Obtaining the activity coefficient of an individual ion 82\u003c\/p\u003e \u003cp\u003e3.5.5. Ionic strength 82\u003c\/p\u003e \u003cp\u003e3.6. Curves of molar variables as a function of the composition in binary systems of a solution with two components  83\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 4. STATISTICS OF OBJECT COLLECTIONS  87\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1. The need to statistically process a system  87\u003c\/p\u003e \u003cp\u003e4.1.1. Collections, system description – Stirling’s approximation  87\u003c\/p\u003e \u003cp\u003e4.1.2. Statistical description hypothesis 88\u003c\/p\u003e \u003cp\u003e4.1.3. The Boltzmann principle  89\u003c\/p\u003e \u003cp\u003e4.2. Statistical effects of distinguishable non-quantum elements  89\u003c\/p\u003e \u003cp\u003e4.2.1. Distribution law 90\u003c\/p\u003e \u003cp\u003e4.2.2. Calculation of  91\u003c\/p\u003e \u003cp\u003e4.2.3. Determining coefficient  92\u003c\/p\u003e \u003cp\u003e4.2.4. Energy input to a system  95\u003c\/p\u003e \u003cp\u003e4.2.5. The Boltzmann principle for entropy  96\u003c\/p\u003e \u003cp\u003e4.3. The quantum description and space of phases 97\u003c\/p\u003e \u003cp\u003e4.3.1. Wave functions and energy levels  97\u003c\/p\u003e \u003cp\u003e4.3.2. Space of phases: discernibility of objects and states 98\u003c\/p\u003e \u003cp\u003e4.3.3. Localization and non-localization of objects  98\u003c\/p\u003e \u003cp\u003e4.4. Statistical effect of localized quantum objects 99\u003c\/p\u003e \u003cp\u003e4.5. Collections of non-localized quantum objects 100\u003c\/p\u003e \u003cp\u003e4.5.1. Eigen symmetrical and antisymmetric functions of non-localized objects  101\u003c\/p\u003e \u003cp\u003e4.5.2. Statistics of non-localized elements with symmetrical wave functions 103\u003c\/p\u003e \u003cp\u003e4.5.3. Statistics of non-localized elements with an asymmetric function  105\u003c\/p\u003e \u003cp\u003e4.5.4. Classical limiting case 107\u003c\/p\u003e \u003cp\u003e4.6. Systems composed of different particles without interactions 107\u003c\/p\u003e \u003cp\u003e4.7. Unicity of coefficient  108\u003c\/p\u003e \u003cp\u003e4.8. Determining coefficient in quantum statistics  110\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 5. CANONICAL ENSEMBLES AND THERMODYNAMIC FUNCTIONS 113\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1. An ensemble 113\u003c\/p\u003e \u003cp\u003e5.2. Canonical ensemble 114\u003c\/p\u003e \u003cp\u003e5.2.1. Description of a canonical ensemble 114\u003c\/p\u003e \u003cp\u003e5.2.2. Law of distribution in a canonical ensemble  115\u003c\/p\u003e \u003cp\u003e5.2.3. Canonical partition function  116\u003c\/p\u003e \u003cp\u003e5.3. Molecular partition functions and canonical partition functions 117\u003c\/p\u003e \u003cp\u003e5.3.1. Canonical partition functions for ensembles of discernable molecules  117\u003c\/p\u003e \u003cp\u003e5.3.2. Canonical partition functions of indiscernible molecules  118\u003c\/p\u003e \u003cp\u003e5.4. Thermodynamic functions and the canonical partition function 120\u003c\/p\u003e \u003cp\u003e5.4.1. Expression of internal energy 120\u003c\/p\u003e \u003cp\u003e5.4.2. Entropy and canonical partition functions 121\u003c\/p\u003e \u003cp\u003e5.4.3. Expressing other thermodynamic functions and thermodynamic coefficients in the canonical ensemble 123\u003c\/p\u003e \u003cp\u003e5.5. Absolute activity of a constituent 125\u003c\/p\u003e \u003cp\u003e5.6. Other ensembles of systems and associated characteristic functions  127\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 6. MOLECULAR PARTITION FUNCTIONS 131\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1. Definition of the molecular partition function  131\u003c\/p\u003e \u003cp\u003e6.2. Decomposition of the molecular partition function into partial partition functions 131\u003c\/p\u003e \u003cp\u003e6.3. Energy level and thermal agitation 133\u003c\/p\u003e \u003cp\u003e6.4. Translational partition functions  134\u003c\/p\u003e \u003cp\u003e6.4.1. Translational partition function with the only constraint being the recipient 135\u003c\/p\u003e \u003cp\u003e6.4.2. Translational partition function with the constraint being a potential centered and the container walls  137\u003c\/p\u003e \u003cp\u003e6.5. Maxwell distribution laws  139\u003c\/p\u003e \u003cp\u003e6.5.1. Distribution of ideal gas molecules in volume 139\u003c\/p\u003e \u003cp\u003e6.5.2. Distribution of ideal gas molecules in velocity 140\u003c\/p\u003e \u003cp\u003e6.6. Internal partition functions 142\u003c\/p\u003e \u003cp\u003e6.6.1. Vibrational partition function 142\u003c\/p\u003e \u003cp\u003e6.6.2. Rotational partition function  144\u003c\/p\u003e \u003cp\u003e6.6.3. Nuclear partition function and correction of symmetry due to nuclear spin 146\u003c\/p\u003e \u003cp\u003e6.6.4. Electronic partition function  149\u003c\/p\u003e \u003cp\u003e6.7. Partition function of an ideal gas  149\u003c\/p\u003e \u003cp\u003e6.8. Average energy and equipartition of energy 150\u003c\/p\u003e \u003cp\u003e6.8.1. Mean translational energy 151\u003c\/p\u003e \u003cp\u003e6.8.2. Mean rotational energy 152\u003c\/p\u003e \u003cp\u003e6.8.3. Mean vibrational energy  152\u003c\/p\u003e \u003cp\u003e6.9. Translational partition function and quantum mechanics 153\u003c\/p\u003e \u003cp\u003e6.10. Interactions between species 155\u003c\/p\u003e \u003cp\u003e6.10.1. Interactions between charged particles 155\u003c\/p\u003e \u003cp\u003e6.10.2. Interaction energy between two neutral molecules  156\u003c\/p\u003e \u003cp\u003e6.11. Equilibrium constants and molecular partition functions 161\u003c\/p\u003e \u003cp\u003e6.11.1. Gaseous phase homogeneous equilibria  162\u003c\/p\u003e \u003cp\u003e6.11.2. Liquid phase homogeneous equilibria 164\u003c\/p\u003e \u003cp\u003e6.11.3. Solid phase homogenous equilibria 166\u003c\/p\u003e \u003cp\u003e6.12. Conclusion on the macroscopic modeling of phases 167\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 7. PURE REAL GASES 169\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1. The three states of the pure compound: critical point  169\u003c\/p\u003e \u003cp\u003e7.2. Standard state of a molecular substance  170\u003c\/p\u003e \u003cp\u003e7.3. Real gas – macroscopic description  171\u003c\/p\u003e \u003cp\u003e7.3.1. Pure gas diagram (P-V) 171\u003c\/p\u003e \u003cp\u003e7.3.2. “Cubic” state equations 172\u003c\/p\u003e \u003cp\u003e7.3.3. Other state equations  177\u003c\/p\u003e \u003cp\u003e7.3.4. The theorem of corresponding states and the generalized compressibility chart  180\u003c\/p\u003e \u003cp\u003e7.3.5. Molar Gibbs energy or chemical potential of a real gas 182\u003c\/p\u003e \u003cp\u003e7.3.6. Fugacity of a real gas  183\u003c\/p\u003e \u003cp\u003e7.3.7. Heat capacities of gases  186\u003c\/p\u003e \u003cp\u003e7.4. Microscopic description of a real gas 188\u003c\/p\u003e \u003cp\u003e7.4.1. Canonical partition function of a fluid  188\u003c\/p\u003e \u003cp\u003e7.4.2. Helmholtz energy and development of the virial 195\u003c\/p\u003e \u003cp\u003e7.4.3. Forms of the second coefficient of the virial  197\u003c\/p\u003e \u003cp\u003e7.4.4. Macroscopic state equations and microscopic description  202\u003c\/p\u003e \u003cp\u003e7.4.5. Chemical potential and fugacity of a real gas 203\u003c\/p\u003e \u003cp\u003e7.4.6. Conclusion on microscopic modeling of a real gas  204\u003c\/p\u003e \u003cp\u003e7.5. Microscopic approach of the heat capacity of gases  206\u003c\/p\u003e \u003cp\u003e7.5.1. Classical theorem from the equipartition of energy  207\u003c\/p\u003e \u003cp\u003e7.5.2. Quantum theorem of heat capacity at constant volume  208\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 8. GAS MIXTURES  213\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1. Macroscopic modeling of gas mixtures 213\u003c\/p\u003e \u003cp\u003e8.1.1. Perfect solutions of perfect gases 213\u003c\/p\u003e \u003cp\u003e8.1.2. Mixture of real gases  215\u003c\/p\u003e \u003cp\u003e8.2. Characterizing gas mixtures  217\u003c\/p\u003e \u003cp\u003e8.2.1. Method of the state equations of gas mixtures 218\u003c\/p\u003e \u003cp\u003e8.2.2. The Beattie–Bridgeman state equation 218\u003c\/p\u003e \u003cp\u003e8.2.3. Calculating the compressibility coefficient of a mixture 222\u003c\/p\u003e \u003cp\u003e8.2.4. Method using activity coefficients of solutions  225\u003c\/p\u003e \u003cp\u003e8.3. Determining activity coefficients of a solution from an equation of state  225\u003c\/p\u003e \u003cp\u003e8.3.1. Methodology 226\u003c\/p\u003e \u003cp\u003e8.3.2. Studying solutions using the PSRK method  227\u003c\/p\u003e \u003cp\u003e8.3.3. VTPR Model 230\u003c\/p\u003e \u003cp\u003e8.3.4. VGTPR Model 233\u003c\/p\u003e \u003cp\u003eAPPENDICES 237\u003c\/p\u003e \u003cp\u003eAPPENDIX 1 239\u003c\/p\u003e \u003cp\u003eAPPENDIX 2 243\u003c\/p\u003e \u003cp\u003eAPPENDIX 3 245\u003c\/p\u003e \u003cp\u003eAPPENDIX 4 253\u003c\/p\u003e \u003cp\u003eAPPENDIX 5 257\u003c\/p\u003e \u003cp\u003eBIBLIOGRAPHY 261\u003c\/p\u003e \u003cp\u003eINDEX 265\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Chemistry [\u003ca title=\"See our other books on Chemistry\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Chemistry%20%5BPN%5D%22\"\u003ePN\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley-ISTE","offers":[{"title":"Brand New","offer_id":52449398980888,"sku":"9781848218642","price":102.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781848218642.jpg?v=1785198101","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/phase-modeling-tools-applications-to-gases-hardback-9781848218642","provider":"Freshly Printed Books","version":"1.0","type":"link"}