課程名稱︰普通物理學甲(上)
課程性質︰大一共同必修
課程教師︰高涌泉
開課學院：理學院
開課系所︰物理系
考試日期（年月日）︰98/01/14
考試時限（分鐘）：110
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(10 pts) Suppose that a father is 20 years older than his daughter. He
wants to travel outward from Earth for 2 years and then back to Earth for
another 2 years (both intervals as he measures them) such that he is then
40 years younger than his daughter. What cocstant speed parameter β
(relative to Earth) is required for the trip?
2.(10 pts) A platform has a proper length of 200m. A train takes 0.5μs to
travel from one end of the platform to the other, as measured by the train
driver.What is the relative speed?
3.(15 pts) A moving proton collides with another proton which is initially
at rest. Calculate the minimum kinetic energy that the moving proton must
_
have in order to make possible the reaction p+p →p+p+p+p .
_
The antiproton (p) has the same mass as the proton. Express your answer
as the ratio of the kinetic energy to the rest energy of the proton.
4.(15 pts) Consider the adiabatic expansion of an ideal gas. Prove that the
relation between the pressure and the volume during such an expansion is
γ Cp
PV = a constant in which γ=----.
Cv
5.(10 pts) Suppose that n moles of oxygen (O2) gas is heated at constant
atmospheric pressure from T1。C to T2。C.
(a) How much energy is transferred to the oxygen as heat? (The molecules
rotate but do not oscillate.)
(b) What fraction of the heat is used to raise the internal energy of
the oxygen?
6.(10 pts) Consider the free expansion of n moles of O2 gas from volume
Vi to volume Vf. What is the entropy change of the gas for this irreversible
process?
7.(30 pts)
(a) What is a Carnot engine?
(b) What is the efficiency of a Carnot engine?
(c) Show that no real engine can have an efficiency greater than that of
a Carnot engine when both engines work between the same 2 temperatures.
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