課程名稱︰普通物理甲上
課程性質︰選修
課程教師︰張寶棣
開課學院：電資學院
開課系所︰資工系
考試日期（年月日）︰2010.1.14
考試時限（分鐘）：120分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題：
1. A long rope with a mass per unit length of 0.1 Kg/m is under a constant
tension of 10 N. A motor at the point x = 0 drives one end of the rope with
harmonic motion at 5 oscillations per second and an amplitude of 4 cm.
(10%)
(a) What is the wave speed?
(b) What is the wavelength?
(c) What is the maximum transverse linear momentum of a 1-mm segment of the
rope?
(d) What is the maximum net force on a 1-mm segment of the rope?
2. Hovering over the pit of hell, the devil observes that as a student falls
past (within terminal velocity), the frequency of his scream decreases from
842 to 820 Hz. Assume that the speed of sound is 343 m/s. (10%)
(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.
3. A string fastened at both ends has successive resonances with wavelengths
of 0.54 m for the nth harmonic and 0.48 m for the (n+1)th harmonic. (10%)
(a) Which harmonics are these?
(b) What is the length of the string?
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 of the pond at 4.0℃. If the
total depth of ice + water is 1.4 m, how thick is the ice? (10%)
(Assume that the thermal conductivities of ice and water are 0.50 and
0.12 cal/m·℃·s, respectively.)
5. Carbon monoxide and oxygen combine to form carbon dioxide with an energy
released of 280 kJ/mol of CO according to the reaction 2(CO) + 02 → 2 CO2.
Two mol of CO and 1 mol of 02 at 300 K are confined in an 80-L container;
the combustion reaction is initiated with a spark. (15%)
(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?
6. 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 terms of p and V. (20%)
(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).
(d) the change in entropy of the gas, S(f) － S(i).
7. Suppose that two heat engines are connected in series, such that the heat
exhaust of the first engine is used as the heat input of the second engine
as shown in Fig. 1. The efficiencies of the engines are ε1 and ε2,
respectively. (10%)
(a) Please express the net efficiency (εnet) of the combination in terms
of ε1 and ε2.
(b) If the two heat engines are ideal reversible show that net
εnet = 1 - Tc/Th
8. (a) What is equipartition principle? (5%)
(b) From a microscopic point view, please explain in words why the entropy
in a close system is maximized. (5%)
(c) List at least three differences between particles and waves. (5%)
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