課程名稱︰普通物理學乙
課程性質︰選修
課程教師︰梁啟德
開課系所︰職治系
考試時間︰94/6/22 15:30-17:20
試題 :
Final examination(22/6/2005)
1.Please prove that for an adiabatic(絕熱) expansion(膨脹) of an ideal gas,
the pressure p and the volume V obey pV^γ＝ a constant, where γ＝Cp/Cv
is the ratio of the molar specific heats(莫耳比熱) for the gas. Cp is the
molar specific heat for a constant pressure process and Cv is the molar
specific heat for a constant colume process, respectively. (10%)
2.If the temperature of a rod of length L is raised by an amount of ΔT, its
lenghth is found to increase by an amount ΔL＝LαΔT, where α is a
constant called the coefficient of linear expansion. Please prove that the
coefficient of volume expansion β is given by β＝3α. (10%)
3.A toy rocket moves at a speed of 242 m/s directly toward a stationary pole
while emitting sound waves at frequency f＝1250 Hz (a) What frequency f' is
sensed by a detector that is attached to the pole? [5%] (b) Some of the
sound reaching the pole reflects back to the rocket, which has an onboard
detector. What frequency f" does it detect? [5%] [Hint: The speed of sound
is 343 m/s. Please consider the Doppler effect 都卜勒效應]
4.Please desing an experiment (設計實驗) to measure the ratio of the charge
to the mass of an electon (電子之電荷與電子質量之比值)(10%)
5.A certain X-ray tube operates a cureent of 7.0 mA and a potential
difference of 80 kV. What is its power(功率) in Watt? (10%)
6.Hall effect two-dimensions (二維系統之難爾效應). Please prove that in a
two-dimensional(2D) electron system, the Hall resistance (霍爾電阻) is given
by R＝V/I＝B/(ne), where V is the Hall potential difference, I is the
current, B is the applied magnetic field perpendicular to the 2D electron
system, n is the carrier concentration (in m^-2) and e is the electron
charge, respectively. (10%)(In 2D, the current density is given by J＝I/w
where w is the width of the 2D system. Ohm's law is given by E＝ρJ, where
ρ＝R is the Hall resistivity in 2D.)
7.A vertical (垂直) spring stretches 9.6 cm when a 1.3 kg block is hung from
its end. (a) Calculate the spring constant.(5%) This block is then displaced
an additional 5.0 cm downward and released from rest. Find (b) the period(5%)
(c) the requency (5%) and (d) the amplitude(5%) of the resulting Simple
Harmonic Motion (SHM)(簡諧運動)
8.A parallel-plate capacitor (平行板電容器) whose capacitance C (電容) is 13.5
pF (1 pF＝1 x 10^-12 Farad) is charged to a potential difference V＝12.5 V
between its plates. What is the melectric potential energy (電位能) of this
ccapacitor. (10%)
9.Please prove that the period T of a simple pdndulum (with small amplitude)
is given by T＝2π√(L/g) where L is the massless string of length and g is
the free-fall acceleration. (10%)
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