※ [本文轉錄自 NTU-Exam 看板] 作者: Lycca (Lycca) 看板: NTU-Exam 標題: [試題] 94下 普通物理學甲下 張寶棣 資工系 時間: Fri Mar 31 20:41:08 2006 課程名稱︰普通物理學甲下 課程性質︰系上必修 課程教師︰張寶棣 開課系所︰資工系 考試時間︰很久(說是 10:20 ~ 12:30 但據說 13:20後還可以繼續考) 試題 : 1. A vertical closed cylinder of cross-sectional area A is dvivied into two equal parts temperature T_1 and pressure p_1 , and the bottom part is filled with oxygen at a temperature 2T_1. The cylinder is turned upside- down. To keep the piston in the middle, the oxygen must be cooled to T_2 = T_1/3 , with the temperature of nitrogen at T_1 , Find the initial pres- sure of oxygen p_i. ( 10 % ) 2. An aluminum pipe, 0.655m long at 20.0 C and open at both ends, is used as a flute. The pipe is cooled to a low temperature but then is filled with an air at 20.0 C as soon as you start to play it. After that, how much does its fundamental frequency, changes as the metal rises in temperature from 5.00 C to 20.0 C ? ( The thermal expansion coefficient for aluminum is 24 X 10 ^ -6 C^-1 ) ( 10% ) 3. A steam pipe of length L is insulated with a layer of material of thermal conductivity k. Find the rate of heat transfer if the temperature outside the insulation is t_1, the temperature inside is t_2, the outside radius of the insulation is r_1, and inside is r_2 ( 10% ) 4. In an isothermal expansion, an ideal gas at an initial pressure P_0 expands until it's volume is twice its initial volume. (a) Find its pressure after the expansion. (b) The gas is then compressed adiabatically and quasi-stat- ically back to its original volume, at which point its pressure is 1.32 P_0 Is the gas monatomic, diatomic or polyatomic? (c)How does the translational kinetic energy of th gas change in these processes? ( 15% ) 5. A mass m initially at temperature T_1 is placed in thermal contact with an equal mass of the same material initially at temperature T_2. The combina- tions is well insulated from the environment, so that heat transfer occurs only between the two masses. (a) What is the entropy change of the whole system in terms of the specific heat c, T_1, T_2 and mass m? (b) Show that ΔS > 0 . ( 10% ) 6. A mole of a monatomic ideal ideal gas is taken from an initial pressure p and volume V to a final pressure 3p and 3V by two different processes: (I) It expands isothermally until its volume is tripled, and then its pressure is incresed at constant volume to the final pressure. (II)It is compressed isothermally until its pressure is tripled, and then its volume is increase at constant pressure to the final volume. Show the path of each process on a p-V diagram, For each process calcuate, in terms of p and V, (a) the heat absorbed by the gas in each part of the process, (b) the work done by the gas in each part of the process, (c) the change in internal energy of the gas, E_int,f - E_int,i , and (d) the change in entropy of the gas S_f - S_i ( 20% ) 7. The Clausius equation of state is P(V - bn) = nRT , where b is a constant. Show that the efficiency of Carnot cycle is the same for a gas that obeys this equation of stats as it is for one that obeys the ideal-gas equation of state, PV = nRT.( 10% ) 8. State the 0th, 1st and 2nd laws of thermodynamics (5%) 9. Two moles of an ideal gas originally at T = 400 K and V = 40 L undergo a free expansion to twice their initial volume. What is the entropy change? 10. Suppose that two engines are connected in series such that the heat exhaust of the first engine is used as the heat input of the second engine The efficiencies of the engines are ε_1 and ε_2, respectively. Show that the net efficiency of the combination is given by ε_net = ε_1 + (1-ε_2) * ε_2 ( 5% ) --

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