課程名稱︰普通物理學甲上 課程性質︰系必修 課程教師︰張寶棣 開課學院：電機資訊學院 開課系所︰資工系 考試日期（年月日）︰2009/1/16 考試時限（分鐘）：130 min , 10:20-12:30 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1. The equation of a transverse wave traveling along a very lonng string is y = 6.0sin(0.020πx+4.0πt), where x and y are expressed in centimeters and t is in seconds. Determine (a) the amplitude, (b) the wavelength, (c) the frequency, (d) the speed, (e) the direction of the propagation of the wave, (f) the maximum transverse speed of a particle in the string. (g) What is the transverse displacement at x = 3.5cm when t = 0.26s? (15%) 2. To permit measurement if her speed, a skydiver carries a buzzer emitting a steady tone at 1800 Hz. A friend on the ground at the landing site directly below listens to the amplified sound. Assume that the air is calm and that the sound speed is 343 m/s, independent of altitude. While the sky diver is falling at terminal speed, her friend on the ground receives waves of frequency 2150Hz. (a) What is the skydiver's speed of descent? (b) Suppose the skydiver can hear the sound of the buzzer reflected from the ground. What frequency does she receive? (10%) 3. A string fastened at both ends has successive resonances with wavelengths of 0.54 m for the nth harmonic and 0.48m for the (n+1)th harmonic. (a)Which harmonicx are these? (b) What is the length of the string? (10%) 4. Ice has formed on a shallow pond and a steady state has been reached, with the air above ice at -5.0℃ and the bottom if the pond at 4.0℃. If the total depth if ice+water is 1.4 m, how thick is the ice? (Assume that the thermal conductivities of ice and water are 0.50 and 0.12 cal/m‧℃‧s, respectively.) 5.Please prove that p‧V^γ = a constant, where γ = Cp/Cv for an ideal gas under the adiabatic expansion. (5%) 6. Carbon monoxide and oxygen combine to form carbon dioxide with an energy released if 280 KJ/mol of CO according to the reaction 2(CO) + 02 → 2CO2. Two moles of CO and 1 mole of O2 at 300K are confined in an 80-L container; the combustion reaction is initiates with a spark. (a) What is the pressure in the container prior to the reaction? (b) If the reaction proceeds adiabatically, what are the final temperature and pressure? (c) If the resulting CO2 gas is cooled to 0℃, what is the pressure in the container? (15%) 7. A 1.00-mol sample of an ideal monatomic gas is taken through the cycle shown in Fig.1 The process A → B is reversible isothermal expansion. Calculate (a) the net work done by the gas, (b) the energy added to the gas by heat, (c) the energy exhausted from the gas by heat, and (d) the efficiency. (15%) 8. One mol of an ideal monatomic gas, at an initial pressure of 5.00 Kpa, and initial temperature of 600 K, expands from initial volume Vi = 1.00 m^3 to final volume Vf = 2.00 m^3. During the expansion, the pressure p and volume V of the gas are related by p = 5.00exp[(Vi-Vf)/a], where p is in kilopascals, Vi and Vf are in cubic meters, and a = 1.00m^3. What is the change is entropy of the gas during the expansion? (hint: Use two simple reversible processes to find the entropy change.) (10%) 9. A mass m1 with mass specific heat c1 initially at temperatre T1 is placed in thermal contact with another mass m2 with mass specific heat c2 initially at temperature T2. The combinations is well insulated from the environment, so that heat transfer occurs only between the two masses. (a) Prove that the final temperature is equal for m1 and m2 by maximizing the total entropy change. (b) Find the entropy change in terms of c1,c2,T1,T2,m1, and m2? (10%) --

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