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SUPPLEMENT TO CHAPTER 5REVIEW QUESTIONS FOR CHAPTER 5429Supplement to Chapter 5REVIEW QUESTIONS5.1Describe the content of Axioms 1, 2, and 3.5.2Give a precise statement of Axiom 4 (the Second Law).5.3Mathematically, what do we mean when we say that the entropy is extensive?5.4Show that the molar entropy function,s(ε, v), is a convex function.5.5Describe the physical meaning of the three parametersα=∂S/∂N,β=∂S/∂E, andγ=∂S/∂V.5.6Define anempirical temperature.5.7Prove thatβ-1is an empirical temperature.5.8Prove thatγ/βis the equilibrium mechanical pressure.5.9Mathematically, what do we mean when we say thatα,β, andpareintensivevariables?5.10Prove thatβis an intensive variable.5.11If two phases of a simple substance are in equilibrium, how many independent variables are there inthe setα,β, andp?5.12What is a quasistatic process?5.13Prove thatdS= 0 if a substance is slowly compressed in an insulating cylinder.5.14How many arbitrary parameters are there in the entropy function of a simple substance?5.15What is an isothermal curve in theEVplane?5.16Describe how one can determine an isothermal curve.5.17What is an adiabatic curve in theEVplane?5.18Describe how one can determine an adiabatic curve.5.19Using only properties derived from the axioms of thermodynamics and mechanical measurements,describe how one can determine the entropy function of a simple substance.5.20How isSrelated to the energy spectrum of a system (in rational units and in SI units)?5.21What happens to the derivatives of the entropy function at the boundaries of the thermodynamicstate space?5.22Explain how a system can be brought to a negative temperature state.5.23What is Nernst’s law?5.24Show thatS=αN+βE+γV.5.25Derive the Gibbs-Duhem relation.5.26FrompV=NkTandE=32NkT, derive the entropy functionS(N, E, V) for a monatomic ideal gas.5.27Define the canonical potentialϕ, and express its partial derivatives in terms of thermodynamic vari-ables.
SUPPLEMENT TO CHAPTER 5REVIEW QUESTIONS FOR CHAPTER 54305.28Do the same for the grand potentialψ.5.29For a system in contact with a reservoir at coldnessβ, what is the condition that determines theequilibrium state?5.30For a system in contact with an energy reservoir at coldnessβ, write the probability of finding thesystem with energyEin terms of the entropy function of the system.5.31Using the fact that, for a system that can exchange particles with a reservoir, the mean squarefluctuation inNis given by (∆N)2=-∂N/∂α, derive the aﬃnity of the solute for a dilute solution.
SUPPLEMENT TO CHAPTER 5EXERCISE 5.2431EXERCISES

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