Advanced Thermo chap6

Advanced Thermo chap6 - 1 Chapter 6 The Thermodynamics of...

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Unformatted text preview: 1 Chapter 6 The Thermodynamics of Multi-component Mixtures 6.1 The thermodynamic description of mixtures for a C component mixture, the equations of state of the forms: ) ,....... , , , ( ) ,....... , , , ( 1 2 1 2 1- = = C C x x x P T U U N N N P T U U or ) ,....... , , , ( ) ,....... , , , ( 1 2 1 2 1- = = C C x x x P T V V N N N P T V V or The simplest description: linear combination description ) , ( ) ,....... , , , ( 1 1 2 1 = =- C i i i C P T U x x x x P T U ) , ( ) ,....... , , , ( 1 1 2 1 = =- C i i i C P T U x x x x P T U or the descriptions above imply that the internal energy of mixing is zero, which is not true for most of the mixtures. 2 Definition of a Partial molar property ( 29 i j N P T i i i N N x P T = = , , ) , , ( always satisfies i ) , , ( 1 x P T x C i i i = = for example, the partial molar Gibbs free energy is defined as ( 29 j i N P T i i N G N G = , , and ) , , ( 1 x P T G x G C i i i = = proof of the linear combination equality C N N N N + + + = ....... 2 1 N N x i i / = ( 29 + = + = = = = C j j x P T j N P T N P T N P T C C N x x N N N N N N N N N N N N N P T N x x x P T N N j i j j j 2 1 , , , , 1 , , 1 , , 1 3 2 3 2 1 1 1 ) ,....., , , , ( ) ,..... , , , ( N x N N N N N N N N N x j j j j j- =- = = = 2 1 1 1 1 ( 29 - = = C j x P T j j j i x x N N 2 , , 1 also true for V , H , S , A and U 3 ( 29 ( 29 ( 29 - + = - +- + = + + = + = + = = = = = C k x P T k k x P T j C j k k x P T k k j x P T j C j k k j k x P T k j j x P T j C k j j x P T j N P T j N P T j N P T j k i j i k i j i k i j i j i j i j i j i x x x x x x x N x x N N x x N N N N x N N N N N N N 2 , , , , , 2 , , , , , 2 , , , , 2 , , , , , , , , 1 for 1 j - + + - = = = = = C l C k k k l l l l C j j j k C k k x x x x x x x x x x x 2 2 2 1 1 1 ( 29 = - + = - - + = = = = = = = = = = 1 2 2 2 2 2 2 2 1 1 1 C l C k k k l C l C k k k l C l C k k k l C k k k C l l k C k k x x x x x x x x x x x x x x 4 isothermal volume change on mixing [ ] - = - = - = = = = = C i i i i C i i i C i i i C i i i C C mix P T V x P T V N P T V N x P T V x N P T V N N N N P T V N N N P T V 1 1 1 1 2 1 2 1 ) , ( ) , , ( ) , ( ) , , ( ) , ( ) ,...., , , , ( ) ,...., , , , ( [ ] - = - = - = = = = = C i i i i C i i i C i i i C i i i...
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Advanced Thermo chap6 - 1 Chapter 6 The Thermodynamics of...

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