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Consider a system that undergoes a phase change from phase a to phase B at equilibrium temperature To and α equilibrium pressure P. At these equilibrium conditions, the heat absorbed per mole of material undergoing this transition is 90, and there is a molar volume change of AV.m. The molar heat capacities at constant pressure for the a and ß phases are Cp,m,& and Cp,m.b; they are inde- pendent of temperature. a. Evaluate w, AU, A H, AS, and AG for converting 1 mol of the system from phase a to phase B at the equilibrium To and P4. Your answer should be in terms of 9", AV.p.m, etc. b. Evaluate ApH and ApS at temperature T* different from To, but at the same pressure Po. c. The denaturation transition of a globular protein can be approximated as a phase change a to B. Calcu- late AgGº, A&Hº, and Apsº for a heat of transition = 638 kJ mol at To = 70°C Po " = 70°C Po = 1 bar; Cp.m,c – Cp.m.b = 8.37 kJ mol-'K-! - of 90
d. Calculate A,G,A,H, and A S for the same transition at 37°C and 1 bar. Assume that Cp.m,a – Cp.m.b is indepen- dent of temperature. e. If Av. for the transition is +3 mL mol"!, will the equilibrium transition temperature to be increased or decreased at a pressure of 1000 bar? Explain. f. Write a thermodynamic cycle that would allow you to calculate the equilibrium transition temperature corre- sponding to a pressure of 1000 bar. Use the cycle to write an equation that in principle could be solved to calculate To at 1000 bar.