課程名稱︰物理化學一-熱力學 課程性質︰必修 課程教師︰陸駿逸 開課學院：理學院 開課系所︰化學系 考試日期（年月日）︰2012/11/09 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.Carnot's theorem says that no engine working with two heat reservoirs (at T_H, T_C)is more efficient than the Carnot engine. How does this lead to the Clausius inequality Q_H/T_H + Q_C/T_C ≦0? 2.Derive the expression for (∂U/∂V)_T,n for a gas following the virial equation with PV/nRT = 1 + nB/V. 3.At very low temperature, the conducting metal has the heat capacity C_p(t) = aT + bT^3. Calculate its entropy S(T). 4.The nature uranium contains 0.7% of U-235. At room temperature, estimate the minima work required to separate 0.007mole of pure U-235 from one mole naturaluranium? 5.Derive the following relations: (1) ╭ ∂H ╮ ╭ ∂G ╮ │───│ = │───│ ╰ ∂P ╯S,n ╰ ∂P ╯T,n (2) ╭ ∂S ╮ ╭ ∂V ╮ │── ─│ = -│───│ ╰ ∂P ╯T,n ╰ ∂T ╯P,n 6.Given the following fundamentalrelation of a thermodynamics system S = R(UV/n - n^3/UV) where the notation follows the lecture. Calculate (1) the internal energy U(T,V,n); (2) the equation of state P(T,V,n); (3) the Helmholtz free energy A(T,V,n). 7.Suppose that a gas obeys P = nRT/(V-nb) + an^2/(TV^2) Calculate (∂C_v/∂V)_T,n. --

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