L10 - ChemicalPotential-Review

# L10 - ChemicalPotential-Review - PH2103 Thermal Physics...

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PH2103 Thermal Physics Mid-term exam Monday 21 st September Hall C - Block N2-B2C-12 Open book exam (everything but electronic devices)

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PH2103 Thermal Physics Lecture 10: Chemical potential & review Massimo Pia Ciamarra [email protected] SPMS-PAP-03-14 Textbook paragraph: 3.4 Discussion Forum
1. Diffusive equilibrium Chemical potential 2. Review Concepts Exercises Agenda

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1. Diffusive equilibrium Chemical potential
Entropy A system in thermodynamic equilibrium is in the macrostate with the largest entropy – i.e. we the largest value of Where is the number of microstates corresponding to a given macrostates. A convenient property of the entropy is its additive character. If a system is made of two subsystems, then This allows to relates macroscopic and microscopic quantities. S = k log Ω S = S A + S B

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Entropy Consider for instance, the equilibrium with respect to a generic conserved quantity X A (this could be V A , or U A , or N A ). Conserved means: X A + X B = const, and therefore dX A = -dX B . (e.g. if the volume of A increase by some amount, the volume of B decreases by the same amount). Entropy is additive: Entropy is maximal: S = S A + S B dS dX A = dS A dX A + dS B dX A = 0 dS A dX A = dS B dX B Equilibrium condition With respect to variable X
What we have done: Temperature Equilibrium with respect to the exchange of energy: Pressure Equilibrium with respect to the exchange of volume: dS A dV A = dS B dV B dS A dU A = dS B dU B and T A = T B T = U S and P A = P B P = T S V

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Diffusive equilibrium We now consider two systems, A and B, that are free to exchange particles and energy. The two systems are made of the same species of particles.
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