6. Recall from our discussions on thermodynamics the temperature and pressure dependence of the Gibbs free energy DAG=AV

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6 Recall From Our Discussions On Thermodynamics The Temperature And Pressure Dependence Of The Gibbs Free Energy Dag Av 1 (54.15 KiB) Viewed 21 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 aG =AV and ap DAG =-AS, IF AV and AS were independent of temperature, then one could trivially calculate AG across any pressure or temperature range (when the other is held constant): az AG, = AG+AVP - P.) AG, - AG-AST-1) (a) T (b) 1 d=f(x)(x-x)+. DAS AC As you already know, in general AS depends on temperature, namely at 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 AV temperature is known as the (isothermal) compressibility: = AB. Apply a др Taylor series expansion to AG : f(x) = f(x) + f(x) (x-x)+ do 2! dx What are the assumptions in the new expression? Neither AG, nor AG, is universal in that phase transition lines (where AG(P.1)=0) traverse p-7 space in two dimensions. We need a general expression for AG(p. 7). To do (аду ans So, we need to incorporate some information about and which turns ат др op out to be supplied by the phase line To proceed, we invoke the Clapeyron ar equation, which applies generally: (c) dp AH dT TAV Show that др ат AS AV 00