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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