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Lecture 32—Grand canonical ensemble Chapters 9, Wednesday April 2 nd

Lecture 32—Grand canonical ensemble Chapters 9, Wednesday April 2 nd. Systems with variable particle number Conditions for equilibrium Revised 1st and 2nd laws Chemical and Gibbs potentials Calculating the chemical potential Examples. Reading: All of chapter 9 (pages 188 - 207)

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Lecture 32—Grand canonical ensemble Chapters 9, Wednesday April 2 nd

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  1. Lecture 32—Grand canonical ensemble Chapters 9, Wednesday April 2nd • Systems with variable particle number • Conditions for equilibrium • Revised 1st and 2nd laws • Chemical and Gibbs potentials • Calculating the chemical potential • Examples Reading: All of chapter 9 (pages 188 - 207) Homework 9 due Wed. Apr. 9th at 5pm Assigned problems, Ch. 9: 2, 4, 6, 8, 10

  2. Chapter 9: systems with variable #s of particles Chemical reaction:

  3. London – van der Waals’ interaction Repulsion occurs when the negative electron clouds eventually come into contact. It is a very hard interaction, almost like the collision between two billiard balls, i.e. V increases very rapidly. Etotal = K + V = constant Lennard-Jones potential r0

  4. London – van der Waals’ interaction Thus, we need to modify the combined 1st and 2nd laws: dU = TdS – PdV + mdN Etotal = K + V = constant • So, the addition of particles to a system results in the addition of kinetic energy to the system which almost immediately dissipates to the entire system. • Therefore, the addition of particles changes the internal energy of the system. The change in the internal energy dU is proportional to the number of particles dN that are added. The proportionality constant m is called the ‘chemical potential’.

  5. The combined 1st and 2nd Laws If more than one type of particle (constituent) is added, then

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