課程名稱︰物理化學一 課程性質︰化學系系必修 課程教師︰李弘文 開課學院：理學院 開課系所︰化學系 考試日期（年月日）︰2009.03.27 考試時限（分鐘）： 08:10~10:10，120分鐘 是否需發放獎勵金：是 試題 : 備註：文章中δ均代表偏微分符號 Ⅰ. True(T) / False(F) (40 pts, 2 pts for each question) For something to be true, it has to be always true. (a) The energy of an isolated system is constant. (b) The same number of O2 gas molecules are put into two containers (big and small) at the same temperature. The gas in smaller container has higher Vrms speed. (c) In an adiabatic process, there is no heat exchange; therefore the temperature is constant. (d) When the temperature of an ideal gas doubles from 50℃ to 100℃, the average kinetic energy is also doubled. (e) If a system expands irriversibly at constant temperature, w = -q . irrev (f) No work can be done from an isothermal cyclic process. (g) A reversible process in an isolated system is spontaneous. (h) Area under P-V curve is the work done in the gas expansion process, but area under T-S curve only equals to the heat of the reversible process. (i) T is an intensive property, but U is an extensive property. (j) When two ideal gases are mixed together in a container under constant pressure, the entropy of the universe is constant for this process. (k) (-PdV) is an exact differential. (l) If He gas has the same speed as Ar gas, it must have the same temperature. (m) To heat up gas at constant pressure, syste, must do work to the surrounding. (n) Joule-Thomson experiment is a constant enthalpy process. (o) van der Waals gas cools upon compressoin when the temperature is below its inversion temperature. This can be used to liquify gases. (p) Claucius inequality says that ∮δq/T ≦ 0. (q) ΔS = ΔH / T for any reversible process at constant pressure. (r) The analysis of a Carnot engine suggests that hotter engine is more efficient. (s) If the compressibility factor Z for a real gas is smaller than one, the gas is less compressible than the ideal gas. (t) Two different adiabatic processes cannot cross in the P-V curve. Ⅱ. Long qustions (70 points) 1. (20 pts, 5 pts each) [You have to answer all signs correctly in each process to get the points.] For each of the following processes, fill the table for each of the quantities (q, w, ΔU, ΔH, ΔSsys) whether it is positive (+), negative (-), zero (0), or unable to determine (U/D): A). An ideal gas is compressed isothermally with an external pressure roughly equal to the internal pressure. B). Reversible adiabatic expansion of a non-ideal gas following this equation: n 2/3 ( P - a(─) ) V = nRT, where a>0. V C). Equal amount of hot water and cold water is mixed in a thermally insulated, closed container in a fixed volume. (Consider water and bottle together as the system.) D). A sample of gas is carried through a complete, reversible Carnot cycle. ┌───┬───┬───┬───┬───┬───┐ │ │ q │ w │ ΔU │ ΔH │ΔSsys│ ├───┼───┼───┼───┼───┼───┤ │ A │ │ │ │ │ │ ├───┼───┼───┼───┼───┼───┤ │ B │ │ │ │ │ │ ├───┼───┼───┼───┼───┼───┤ │ C │ │ │ │ │ │ ├───┼───┼───┼───┼───┼───┤ │ D │ │ │ │ │ │ └───┴───┴───┴───┴───┴───┘ 2.(8 pts) Stirling engine Most internal conbustion engines generate NOx gas during its high temperature cycle. NOx is closely linked to air pollution/climate change and the regulation of its emission greatly reduces the efficiency of the engine, One alternative is "Stirling engine", which use regeneratable external combustion heat source. Its cycle contains the following steps: 1). Constant Volume heating 2). Isothermal expansion 3). Constant Volume cooling 4). Isothermal compression Plot the P-V curve and T-S curve of this cycle, and label each step in the curve. P↑ T↑ │ │ │ │ │ │ └───→ └───→ V S 3. (6 pts) Gas Kinetic Theory (3 pts)(a) Calculate the root-mean-square speed of Oxygen O2 molecule at 300K (in m/s). (3 pts)(b) Draw a sketch of what you expect the molecular speed distribution functions for O2 at 300 K (solid line, ──) and at 1000 K (dash line, ---). Probability Density ↑ │ │ │ │ └─────────→ Molecular Density (m/s) 4.(4 pts) Which of the following functions is(are) exact differential? (a) z = ln(x/y), (b) z= exp(xy) 5.(8 pts) Calculate the value of ΔS of the following process: 0.5 mole of water(l) at 20℃ and 1 atm →0.5 mole of steam(g) at 110℃ and 1 atm The molar heat of vaporization of water at 373 K is 40.79 KJ/mol, and the molar heat capacity (Cp) of water and steam are 75.3 J/K-mol and 33.6 J/K-mol, respectively. Assume the Cp is a temperature-independent constant, volume of water is neglectable compared to that of steam, and ideal-gas behavior. 6.(8 pts) Two blocks of the same metal of the same size are at different temperatures, T1 and T2. These metal blocks are brought together and allowed to the same temperature. Show that the entropy change is given by (T1 + T2)^2 ΔS = Cp ln ────── where Cp is a constant. 4 T1 T2 7.(6 pts) One gram of liquid benzene (C6H6) is burned in an adiabatic bomb calorimeter. The temperatures before and after the ignition were 20.826℃ and 25.000℃. The heat capacity of the bomb, the water around it, and the contents of the bomb after the combustion was 10,000 J/K. Calculate ΔfH0 for C6H6(l) at 298.15K from these data. [Given ΔfH0 (CO2,g): (-393.51 KJ/mol), ΔfH0 (H2O, l): (-285.83 KJ/mol)] 8.(10 pts, 2pts each) A mole of an ideal gas initially at 20℃ is expanded from 2L to 4L. Calculate the q, w, ΔU, ΔH, ΔSsys change when this process is carried out isothermally and irriversibly against an external pressure of 2 atm. -----試題結束，以下是答案----- Ⅰ: TFFFT FFTTF FFTTF TFTFT Ⅱ 1. ┌───┬───┬───┬───┬───┬───┐ │ │ q │ w │ ΔU │ ΔH │ΔSsys│ ├───┼───┼───┼───┼───┼───┤ │ A │ - │ + │ 0 │ 0 │ - │ ├───┼───┼───┼───┼───┼───┤ │ B │ 0 │ - │ - │ U/D │ 0 │ ├───┼───┼───┼───┼───┼───┤ │ C │ 0 │ 0 │ 0 │ 0 │ + │ ├───┼───┼───┼───┼───┼───┤ │ D │ + │ - │ 0 │ 0 │ 0 │ └───┴───┴───┴───┴───┴───┘ 2.圖略 P-V (2)(4): PV = nRT (1)(3): perpendicular to x-axis T-S (1)(3): Sα ln T (2)(4): parallel to x-axis 3.圖略 Vrms(300K) = 483.56 m/s 4.(a)(b) 5.ΔS = 64.21 J/K 6.略 7.ΔfH0 (C6H6, l) = 40.88 KJ/mol 8.q = 404J, w = -404J , ΔU = 0, ΔH = 0, ΔSsys = 5.76 J/K(有爭議) --

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