L3 Interactions and Implications.pdf - Chapter 3...

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Chapter 3 Interactions and Implications These notes are by courtesy of Prof. Brad Foreman
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Outline of this Chapter 1. Temperature and Thermal Equilibrium 2. Entropy and Heat 3. Paramagnetic solid 4. Mechanical Equilibrium and Pressure 5. Diffusive Equilibrium and Chemical Potential Phys4050 Thermodynamics and Statistical Physics 2
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Temperature Second law : when two objects A and B are in thermal equilibrium , the total entropy has reached the maximum. From daily experience, thermal equilibrium is reached when the temperature of the two objects are the same, i.e. Phys4050 Thermodynamics and Statistical Physics ? A = ? B 3
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Maximizing the Total Entropy Suppose the entropies of object A and object B are ? A and ? B , then the total entropy ? is maximum with respect to change of energy ? A , Phys4050 Thermodynamics and Statistical Physics ?? ?? A = ?? A ?? A + ?? B ?? A = ?? A ?? A ?? B ?? B = 0 ? B = ? − ? A ⇒ d? A = −d? B ?? A ?? A = ?? B ?? B at equilibrium 4 ? = 𝑘 ln Ω A + 𝑘 ln Ω B = ? A + ? B
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Formal Definition of Temperature Comparing the two conditions in previous two slides, we anticipate that To be more precise, we keep ? and ? fixed and the definition of temperature is: Phys4050 Thermodynamics and Statistical Physics 1 ? A = ?? A ?? A 1 ? B = ?? B ?? B 1 ? = ?? ?? 𝑁,? 5
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Example: Einstein Solid Phys4050 Thermodynamics and Statistical Physics ? = 𝑞ℏ? 6 ? A = 𝑞 A ℏ? ? B = 𝑞 B ℏ? ? = ? A + ? B Ω = Ω A Ω B
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Phys4050 Thermodynamics and Statistical Physics Same slope ?? A ?? A = − ?? B ?? A ? A = ? B ? max 7
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Example: Einstein Solid (Cont.) Suppose 𝑞 A = 60 for solid A (equilibrium), check the slopes from the table: For solid B, 𝑞 B = 40 , ? A = ? B as it should be! Phys4050 Thermodynamics and Statistical Physics ? A ∆? A ∆? A = 61 − 59 ? 160.9 − 157.4 𝑘 = 0.57 ? 𝑘 = 662.5K ? = ℏ? ≈ 0.1eV ? B ∆? B ∆? B = 41 − 39 ? 107.0 − 103.5 𝑘 = 0.57 ? 𝑘 = 662.5K 8
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