Chemistry 635, Thermodynamics and Statistical Thermodynamics Assignment #3 Due: Feb. 2, 2010. This section follows my lecture on “A Postulate-Based Approach to Chemical Thermodynamics”. References are Silvio Salinas, “Introduction to Statistical Physics” Chapter 3, and McQuarrie, “Statistical Mechanics”, Section 1.4. 1. (a) Rearrange the following equation to obtain dS in terms of dU, dV, and dn. (b) Show that € ds =1T du +pT dv. (c) For a monatomic ideal gas we have PV=nRT and € U =32nRT. Use these equations to show that (i) € ∂s∂v u=Rv (ii) € ∂s∂u v=3R2u (iii) € s u,v( )=32R ln u + Rlnv + Rc where “c” is a constant (iv) € S U,V ,n( )=32nR lnUn + nR lnVn + nRc (a fundamental equation). 2. (a) Using appropriate Legendre transformations, derive two additional thermodynamic potentials beyond those discussed in class. 3. (a) Using the additivity property U(λS, λV, λn) = λ U(S, V, n), derive the Euler equation U – TS + pV - µn = 0 This is most easily done by differentiating the additivity property w.r.t. λ and then setting λ=1. (b) From this, derive the Gibbs-Duhem relationship dµ = vdp – sdT 4. For a monatomic ideal gas, start with the result in question 1(c)(iv) above and derive the explicit form for the fundamental equations for (a) the internal energy € dU = TdS − pdV +µdn€ U S,V ,n( )= nnV 23exp23SnR− c (b) the Helmholtz energy € A(T,V ,n) = −nRT lnVn−32nRT ln3RT2+ nRT32− c( ) 5. From the result in question 4(b) derive the equations of state (a) € S = −∂A∂T V ,n= nR lnVn+32nR ln3RT2+ nRc (b) € p =∂A∂V T ,n= .... (c) € µ=∂A∂n T ,V=
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