課程名稱：物理化學一-熱力學 課程性質：化學系大三必修 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）：106/11/7 考試時限（分鐘）：130 試題： (1) (20 pts) Given the van der Waals' equation of state nRT n^2 P = ——— - a ——— V-nb V^2 (a) Obtain the expression for the second virial coefficient B (where the pressure is a power series of n/V). (b) In terms of a, and b, what is the Boyle temperature for the gas? (c) Derive the formula for the critical temperature and the critical pressure in terms of the parameters a and b. (d) The CO2 has the parameters a = 3.6 atm dm^6 mol^(-2) and b = 4.3 x 10^(-2) dm^3 mol^(-1). Estimate its Boyle temperature, critical temperature and the critical pressure. ( R = 8.3 JK^(-1)mol^(-1) ) (2) (15 pts) Estimate the collision frequency between one hydrogen molecule and the oxygen molecules in this room. From the textbook, the measured collision cross-sections are σ_H2 = 0.27 nm^2, and σ_O2 = 0.40 nm^2. ( Hint : ∫[0,∞] x^2 e^(-x^2) dx = sqrt(π)/4, ∫[0,∞] x^3 e^(-x^2) dx = 1/2, k_B = 1.38 x 10^(-23) JK^(-1) ) (3) (10 pts) Calculate the final pressure of a sample of carbon dioxide that expands reversibly and adiabatically from 67.4 kPa and 0.50 dm^3 to a final volume of 2.00 dm^3. Take γ= 1.4. (4) (10 pts) Calculate ΔS (for the system) when the state of 3.00 mol of perfect gas atoms,for which C_p,m = 2.5R, is changed from 25°C and 1.00 atm to 125°C and 5.00 atm. (5) (10 pts) Someone claims that he has a wonderful engine which, in each cycle, exchanges heat Q_1 = 60J at T_1 = 300K, Q_2 = -10J at T_2 = 200K, Q_3 = -10J at T_3 = 100K. Combine suitable Carnot engine(s), show that the existence of this engine contradicts the Kelvin's version of the second law of thermodynamics. ∂G/T (6) (15 pts) Show that ( ———— )_p,n = H. ∂1/T (7) (10 pts) Show that ( ∂T/∂p )_s = ( ∂V/∂S )_p. (8) (20 pts) Consider N molecules which are confined in a 2D box of length L in the both directions. (a) Count the number of the microstates (Ω) which have the energy within the given range (E,E+ΔE) using the quantum numbers (n_1x,n_1y,...,n_Ny). Use the Boltzmann entropy formula S = k_B lnΩ, to derive the expression for the entropy. (b) Calculate the chemical potential μ = -T ( ∂S/∂N )_E,L. π^(n/2) ( Hint : n dimensional sphere has the volume ————— radius^n. ) (n/2)! --

※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 112.104.140.187 ※ 文章網址: https://webptt.com/m.aspx?n=bbs/NTU-Exam/M.1510939307.A.D93.html