課程名稱︰ 物理化學一 課程性質︰ 必修 課程教師︰ 戴子安 開課學院： 工學院 開課系所︰ 化工系 考試日期（年月日）︰2011/10/24 考試時限（分鐘）：2小時 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.(20%) Explain the following terms. Use graphs if necessary. a)Show the compressibility factor, Z as a function of pressure and the regions of different Z values where the intermolecular forces dominate. b)What is the Boyle temperature? c)What is the Maxwell construction method to determine the phase diagram for a diagram for a VDW gas? d)Use the compressibility factor to demonstrate that both methane and propane follow the principle of the corresponding states. e)Write down the partial molar volume of component 1 in a mixture of N components. f)Write down the definition of P-V work. g)If PV, surface, eleongation, and electrical works are involved in a system, what is the expression for the 1st law of thermodynamics? h)Describe the Joules' method to measure π and explain the incorrectness in T the conclusion i)Plot the inversion curve in the Joule-Thomson experiment and denote the regions of heating and cooling. ╴ j)Use the equipartition theorem to give the expression of the C for monoatomic V and diatomic molecules. 2.(10%) The composition of the atmosphere is approximately 20% O and 80% N by mass. 2 2 At what height above the surface of the earth would the atmosphere become 10% O and 90% N by mass? Assume that the temperature of the atmosphere is constant 2 2 at 25℃. 3.(10%) RT B C A scientist proposed the following equation of state P= —–—–— Show that _ _2 _3 V V V the equation leads to critical behavior. Find the critical constants of the gas in terms of B and C and an expression for the critical compression factor. 4.(10%) Derive the expression for the VDW constants int terms of the critical constants for the gas. Note that the intermediate steps in driving the fianl result have to be correct in order to get the full points! 5.(10%) An ideal gas undergoes a single-stage expansion against a constant external pressure P at constant temperature from T, P , V to T , P , V ext i i f f a)What is the largest m that can be lifted through the height h in this expansion? b)The system is restored to its initial state in a single-stage compression. What is the smallest mass m' that must fall through the height h to restore the system to its initial state? 6 6 Consider that h=10cm, P =2.5x10 Pa, P =0.75x10 Pa, T=300K, n=1.5mol, and i f R=8.3145 J/mol-K 6.(10%) Show that the Joule-Thomson coefficient for a real gas is not zero in the limit of zero pressure. 7.(10%) a)Derive the equation for the work of reversible isothermal expansion of a van der Waals gas from V to V . 1 2 b)A mole of CH is expanded reversibly form 1L to 50L at 25℃. Calculate the 4(g) work in joules assuming (1)the gas is ideal, (2) the gas obeys the van der 2 2 Waals equation. For CH , a=2.283 L bar/mol , b=0.04278 L/mol, and 4(g) R=0.08314 L-bar/K-mol 8.(15%) 6 1.75moles of a monoatomic ideal gas, initially at 32℃ and 2.5x10 Pa undergoes a two-stage transformation. For each of the stages described in the following lists, calculate the final pressure, as well as q, W, ΔU, and ΔH. Also calculate q, W, ΔU, ΔH for the complete process. a) The gas is expanded isothermally and reversibly until the volume doubles. b)Beginning at the end of the first stage, the temperature is raised to 92℃ at constant volume. --

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