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First Order Phase Transitions

Physics 127b: Statistical MechanicsLecture 3: First Order Phase TransitionsThe van der Waals equation for a gas ishPCaV2i[V b]DNkBT:(1)(The variableais proportional toN2andbtoN, ;Nbconstants).It can be motivated by rewriting it in the formPDNkBTV b aV2(2)TheV bterm comes from estimating the free volume available for the molecules by excludinga hard core contribution, and thea=V2is a reduction in the pressure proportional to the densitysquared, representing the attractive interaction of the molecules. InLecture 2we derived expressionsforNaandNbin terms of the pair corresponding free energy isADAideal NkTln 1 bV aV(3)withAidealthe ideal gas expression. (Actually, if we integratePD .@A=@V/N;Tto getAthereis an integration constant ;T/, and we fix this by comparing with the ideal gas expressionforV!1.) The second term is Ttimes theentropy correctionfrom the excluded volume, andthe third term is theenergy correctionfrom the attractive > Visotherms do not look much different from those for theideal gas.

Lecture 3: First Order Phase Transitions The van der Waals equation for a gas is h PC a V2 i [V−b] DNkBT: (1) (The variable ais proportional to N2 and bto N, i.e. aDN2aNand bDNbNwith a;NbNconstants). It can be motivated by rewriting it in the form PD NkBT V−b − a V2 (2) The V−bterm comes from estimating the “free volume” available ...

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