課程名稱︰物理化學一 熱力學 課程性質︰必修 課程教師︰鄭原忠 開課學院：理學院 開課系所︰化學系 考試日期（年月日）︰2013/10/25 考試時限（分鐘）：110 分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : Physical Chemistry I:Thermodynamics Mid-term Exam #1 Date:10/25/2013 1. (40%)The van der Waals equation of state is given by the equation _2 _ (P+a/V )(V-b)= RT (a)Find the critical temperature of a van der Waals gas in terms of the Waals constants. 2 -2 -1 (b)For carbon monoxide,a=1.505 L bar mol and b=0.03985 L mol .What is the critical temperature of carbon monoxide predicted by the van -2 -1 -1 der Waals equation? (R=8.314*10 L bar K mol ) 2 -2 -1 (c)For nitrogen gas, a=1.408 L bar mol and b=0.03913 L mol. Compare these to the values of carbon monoxide, explain the subtle difference in the values of the van der Waals constants using what you know about the two molecules. (Hint:why a co ＞ a N2 and b co ≒ b N2) (d)Draw an isotherm of the van der Waals equation at a temperature lower than the critical temperature. Note that some of the points on this curve are unphysical. Point out these points on the curve that you draw and explain why. (e)Describe, according to Maxwell's suggestion, how the tie line in a van der Waals isotherm can be constructed. (f)Give an equation to relate the pressure of a system to its Helmholtz free energy. Use this equation to justify the Maxwell construction by comparing the free energy differences going from one end of the tie line to the other end. 　δＵ (g)(10%)Calculate （——） for a van der Waals gas. 　 δＴ　T 。 2. (20%)1 mole of liquid water is vaporized slowly at 100 C and 1 atm (reversible condition). The heat of vaporization of water is -1 40.69 kJ mol . What are the values of (a) reversible work W rev, ─ ─ ─ (b)heat q, (c)ΔＵ, (d)ΔＨ, (e)ΔＳ. (Hint:assume vapor is an ideal gas). 3. (10%)Show that dq=dＵ+ PdV = CvdT + RTd lnV is not an exact different, but dq 　　— = Cvd lnT + Rd lnV is an exact differential. Ｔ 4. (10%)An ideal monoatomic gas at 300K and 1 bar is expanded in a reversible adiabatic process to a final pressure of 0.5 bar. Calculate q per mole, ─ ─ w per mole, ΔＵ, and ΔＨ. 5. (10%)Calculate the change in entropy of and ideal gas in changing from T1 ,P1 to T2 ,P2. 6. (15%)For a one-component system dＵ= TdS -PdV +μdn and Ｕ= TS -PV +μn. Complete the following equations: δＨ δＡ δＳ δＳ (a)（——） = ? (b) （——） = ? (c) （—— ）= ? (d) （——） = ? δＰ S,n δＴ V,n δＰ V,n δＰ T,n　　 δＳ (e)（——） = ? δＶ T,n 7. (5%)Use Legendre transform to derive a thermodynamic potential that has (T,V,μ) as its natural variables. Let's call this function Y = Y(T,V,μ) Give the definition of Y and its total differential. 8. (10%)Calculate ΔＳ and ΔＧ for mixing 2 of H2 with 1 mol of O2 at 300K under conditions where the gases are ideal and no chemical reaction occurs . ※因為PTT沒有辦法打partial的符號,所以用δ來取代 --

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