6 Recall from our discussions on thermodynamics the temperature and pressure dependence of the Gibbs free energy DAG - A

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6 Recall From Our Discussions On Thermodynamics The Temperature And Pressure Dependence Of The Gibbs Free Energy Dag A 1 (46.71 KiB) Viewed 25 times

6 Recall from our discussions on thermodynamics the temperature and pressure dependence of the Gibbs free energy DAG - AVdp-ASIT from which we derive the important partial derivatives 2AG - AP and op OG =-AS IF AV and AS were independent of temperature, then one could trivially ar calculate AG across any pressure or temperature range (when the other is held constant) AG, - AG,+AVP-P) AG, -AG-AS(T-T.) (a) CAS ar (6) aAV 1 d=f(x)(x-x... dor 2! dr As you already know, in general AS depends on temperature, namely Refine the expression for AG, What is an assumption in the new expression? In general, AV is a function of pressure. The pressure derivative of volume at constant temperature is known as the (isothermal) compressibility AB. Apply a Op Taylor series expansion to AG, /(= f(x) Of(x)(x-x)+, What are the assumptions in the new expression? Neither AG, nor AG, is universal in that phase transition lines (where AG(P.1)=0) u traverse p-T space in two dimensions. We need a general expression for AG(p.7). To do aar ans So, we need to incorporate some information about which turns ar ap op out to be supplied by the phase line To proceed, we invoke the Clapeyron equation, which applies generally (c) and OT 30 dp AH dT TAV Show that ਹੈ op ar AS ΔΙ" .