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1 Thermal Physics II Chris Parkes Part 2 A) Thermodynamic Potentials & Maxwell Relations B) Statistical Thermodynamics

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2 Thermodynamic Potentials & Maxwell Relations Maxwell Relations from 1 st Laws for U,H,F,G Heat Capacities Joule-Kelvin Process Joule-Kelvin Co-efficients Inversion Temperature Inversion Curve for Real Gas Practical Joule Kelvin Effect Phase Changes (use of Gibbs function, Phase Diagrams) Clausius Clapeyron Equation Vaporisation Curve 1 st order Phase Transitions 2 nd Order phase Transitions

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3 Thermodynamic Potentials Potential DefinitionFirst Law Internal Energy: U(S,V)dU=Tds-PdV Enthalpy: H(S,P)H=U+PVdH=Tds+VdP Helmholtz fn: F(T,V)F=U-TSdF=-SdT-PdV Gibbs fn: G(T,P)G=U+PV-TSdG=-SdT+VdP

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4 Maxwell Relations First LawMaxwell Relation dU=Tds-PdV dH=Tds+VdP dF=-SdT-PdV dG=-SdT+VdP

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5 Throttling Process P, V, TP’ P P’, V’, T’ Piston

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6 PVT Surface Water expands on freezing (as shown here) Most substances contract

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7 T-P Water Triple point at 612Pa, C -ve slope for ice - water is unusual Actual phase diagram more complex – since also crystalline forms of ice, multiple triple points

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