課程名稱︰普通物理學甲上
課程性質︰必修
課程教師︰張寶棣
開課學院：電資
開課系所︰資工
考試日期（年月日）︰2008/1/18
考試時限（分鐘）：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. Two waves are propagating on the same very long string. A generator at one end of the string creates a wave given by
y = (6.0cm) cos(π/2)[(2.5 m^-1)x + (10.0 s^-1)t]
and one at the oher end creates the wave
y = (6.0cm) cos(π/2)[(2.5 m^-1)x - (10.0 s^-1)t]
(a)Calculate the frequency, wavelength, direction, and speed of each wave.(10%
(b)Find the points on the string at which there is no motion(the nodes) (3%)
(c)At which points is the motion on the string a maximum(the antinodes)? (2%)
2. Hovering over the pit of hell, the devil observes that as a student falls past(wihin terminal velocity), the frequency of his scream decreases from 842 to 820 Hz.
(a)Find the speed of descent of the student.
(b)The student's scream reflects from the bottom of the pit. Find the frequency of the echo as heard by the student.
(c)Find the frequency of the echo as heard by the devil. (15%)
3. A rope of total mass m and length L with uniform density is suspended vertically under gravity g. What is the time interval that a transverse pulse travels the length of the rope?(5%)
4. A pond of water at 0°C is covered with a layer of ice 4.00 cm thick. If the air temperature stays constant at -10.0°C, how long dose it take for the ice thickness to increase to 8.0cm? (10%) (Hint: use dQ/dt = KAΔT/x, where dQ is the incremental energy extracted from the water through the thickness x of ice, which is also the amount required to freeze the thickness of ice. That is, dQ = LpAdx, where p is the density of the ice, A is the area, and L is the latent heat of fusion.)
5. Model air as a diatomic ideal gas with M = 28.9 g/mol. A cylinder with a piston contains 1.20kg of air at 25.0°C and 200 kPa. Energy is transgerred by heat into the system as it is allowed to expand, with the pressure rising to 400 kPa. Throughout the expansion, the relationship between pressure and volume is given by P = CV^(1/2), where C is a constant.(a) Find the initial volume. (b) Find the final volume. (c) Find the final temperature. (d) Find the work done on the air. (e) Find the energy
transferred by heat. (15%)
6. A container holds a mixture of three nonreacting gases: n1 moles of the first gas with molar specific heat at constant volume C1, and so on. Find the molar specific heat at constant volume of the mixture, in terms of the molar specific heats and quantities of the separate gases.(5%)
7. What change in entropy occurs when a 27.9-g ice cube at -12°C is transformed into steam at 115°C?(10%)
8. A mole of a monatomic 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 increased at constant volume to the final pressure.(II) It is compressed isothermally until its pressure is tripled, and then its volume is increased at constant pressure to the final volume. Show the path of each process on a p-V diagram, For each process calculate, in term of p and
V,(a) the heat abosrbed 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, and (d)the change in entropy of the gas.(15%)
9. A mass m1 with mass specific heat c1 initially at temperature 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 entorpy change in terms of c1,c2,T1,T2,m1,and m2.(10%)
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