課程名稱︰物理化學一 課程性質︰必修 課程教師︰林萬寅 開課學院：理學院 開課系所︰化學系 考試日期（年月日）︰08/04/12 考試時限（分鐘）：四小時 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : Procedures for all calculations and the units of the final results must be given. 1. One mole of an ideal gas (Cv = 3R/2), initially at 1.0 atm and 300K, undergoes a reversible cycle containing four steps as shown in fig. 1. (R = 8.31 J/(K*mol). 25% Fig. 1. P(atm) 1.0∣_ _(這兩線交同一點) ∣ ﹨＼(1) (1) isothermal ∣_ _ ﹨ ＼__ (2) (2) isobaric 0.6∣ (4) ＼ ∣(3) (3) isochoric 0.2∣_ _ _ _ ＼」 (4) adiabatic ∟╴╴╴╴╴ Find q, w, △U, and △S foe each step. Also find the efficiency ε of the entire cycle. (ε is defined as the total work done divided by the total input of the heat) RT B C 2. A certain gas obeys the equation of state: P = ─ + ── + ──. (15%) Vm Vm^2 Vm^3 (a) Find the critical constants (Pc, Vc, Tc) in terms of B and C. (b) Find an expression for the fugacity coefficient (ψ) in terms of B and C. (c) If B can be approximated by the empirical equation B(T) = a + b*exp(-c/T^2), find an expression of the Boyle temperature in terms of a, b, and c. 3. A gas obeys the equation of state Vm = RT/P + a㏑T and its Cp is given by Cp = b + cT + dP, where a, b, c, d are constants indep. of T and P. (15%) (a) Find an expression for the Joule-Thomson coefficient (μ). (b) Find the inversion temperature of the gas. (c) Find an expression for Cv. 4. The molar Gibbs free energy of a certain gas is given by Gm = a + bP + RT㏑P, where a, b(= 0.1 L/mol) are constants, and P is the pressure (in atm). One mole of this gas at 300K is compressed isothermally and reversibly from 1 atm to 10 atm. Answer the following questions. (15%) (a) Find the equation of state for this gas. (b) Find q, w, △S, △U, △G, and △A for this compression process. 5. The pressure on a 1-kg block of copper at 0℃ is increased from 1 atm to 1000 atm. Assume that the expansion coefficient (α), the isothermal compressibility (κT) and density (ρ) are constant and equal to 5*10^5 K^(-1), 8*10^(-7) atm^(-1), and 8.9*10^3 kg/(m^3); Cp = 394 J/(K*kg). (15%) (a) Calculate the heat evolved and the work done on the copper block when the compression was performed isothermally and reversibly. (b) Estimate the rise in the temperature of copper if the compression was performed adiabadically and reversibly. (c) Estimate the rise in the temperature of copper if the compression was performed isochorically (constant volume). 6. Prove the following relations. (15%) (α^2)*V*T 1 δV 1 δV (a) κT - κS = ─────, where κT = -─(──) and κS = -─(──) Cp V δP T V δP S δU 1 δV (b) (──) = V*(P*κT - α*T), where α = ─(──) δP T V δT P δH α*T - 1 (c) (──) = ──── δV T κT --

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