4. (a) Answer the following questions about entropy-volume relationships: (i) For a general system, use the Helmholtz fr

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4 A Answer The Following Questions About Entropy Volume Relationships I For A General System Use The Helmholtz Fr 1 (195.01 KiB) Viewed 14 times

4. (a) Answer the following questions about entropy-volume relationships: (i) For a general system, use the Helmholtz free energy as an intermediary to express the derivative as av) in terms of a [4 marks] derivative of the pressure P with respect to temperature T. (ii) Assuming an ideal gas, evaluate your derivative of P, and finally integrate (), to determine the volume dependence of the [4 marks] entropy S of the classical ideal gas. (iii) Comment on your result, and in particular on how an alternative understanding of the s(1) dependence can be achieved on the basis of spatial multiplicity considerations. [4 marks] (b) Consider the following questions about Schottky defects in a solid with N atoms. (i) The temperature, T, of the solid is related to the number of defects, M, as 1 Кв [-In M + In(N – M)] T E where e is the activation energy of one defect. What is the density of defects in the solid, expressed as a function of temperature and the activation energy? (ii) Consider a crystal of NaCl. This material has a melting temperature of 1073K. The activation energy of a single Schottky defect in NaCl is 2.12 eV. Is it possible for this material to host 1 Schottky defect for every 10 atoms? [7 marks] [6 marks]