推 LittleKuu:幫補充:課本是"HOLIDAY"第八版 01/19 09:40
推 tiesto1114:樓上拼錯了...是Halliday... 01/19 14:53
課程名稱︰普通物理學
課程性質︰必修
課程教師︰蔡爾成
開課學院：工學院
開課系所︰工程科學與海洋工程學系
考試日期（年月日）︰97/1/18
考試時限（分鐘）：110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. [10%] At very low temperatures, the molar specific heat Cv of aluminum is
approximately Cv=AT^3. Find the entropy change for n mol of aluminum when
its temperature is raised at constant volume from a very low temperature
T1 to another very low temperature T2.
2. [10%] (a) [3%] An ideal gas initially at pressure Pο undergoes a free
expansion until its volume is 3.00 times it initial volume. What then is
the ratio of its pressure to Pο. (b) [7%] The gas is next slowly and
adiabatically compressed back to its original volume. the pressure after
compression is (3.00)^1/3 Pο.Is the gas monatomic, diatomic, or polyatomic?
3. [10%] A uniform rope of mass m and length L hangs from a ceiling. (a) Show
that the speed of a transverse wave on the rope is a function of y, the
distance from the lower end, and is given by υ=(gy)^1/2. (b) Show that the
time a transverse wave takes to travel the length of the rope is given by
t=2(L/g)^1/2.
4. [10%] Three identical stars of mass M from an equilateral triangle that
rotates around the triangle's center as the stars move in a common circle
about the center. The triangle has edge length L. What is the speed of the
stars?
5. [10%] As shown on the first figure below, a stream of water flowing through
a hole at depth h in a tank holding water to height H. At what distance χ
does the stream strike the floor?
→
6. [10%] In the 2nd figure shown above, what magnitude of force F applied
horizontally at the axle of the wheel is necessary to raise the wheel over
an obstacle of height h. The wheel's radius is r and its mass is m.
7. [10%] It is known that the Maxwell's probability distribution function of
molecular speeds in a gas at temperature T is
M 3/2 2 -Mv^2/2RT
P(v) = 4π(───) v e
2πRT
[5%] (a) What is the most probable speed Vp? (b) [5%] What is the average
∞ -x
speeds ＜υ＞? You may need to make use of the integral ∫xe dx = 1.
0
8. [10%] the equation of motion for a damped oscillator under an external
driven force is
.. ..
mχ + bχ + kχ = F cos(ω t+θ).
o d
Find the resonant steady-state solution χ(t) when mω ^2 = k.
d
9. [10%] The orbit for a planet moving around the Sun is an ellipse whose
semi-major axis (one half the major axis) and semi-minor axis (one half the
major axis) are a and b. If the speed of the planet is υ at the perihelion
(the point that is nearest to the sun), what is the speed of the planet at
the aphelion (the point that is farthest from th sun)? Express your answer
in terms of a, b, υ.
10.[10%] The first Law of thermodynamics for an ideal gas is
dE = dQ - PdV,
int
where dQ represents the energy exchanged as heat between the system and its
surroundings. Show that the amount of heat exchanged between two states may
be path dependent by providing an example. Q therefore can not be a state
function of the ideal gas.
第五題圖可參考第八版課本 p384 65題
第六題圖可參考第八版課本 p323 21題
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