课程名称︰普通物理
课程性质︰化工系必带
课程教师︰梁启德
开课学院：理学院
开课系所︰
考试日期（年月日）︰2016/1/14
考试时限（分钟）：120分钟
试题 :
1.Please prove that for an adiabatic expansion 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 for the gsa. Cp isthe molar specific heat for a constant
pressure process and Cv is the molar specific heat for a constant volume
process, respectively(10%)
2.An elevator repairman(mass=73kg) sits on top of an elevator cabin of mass
655 kg inside a shaft in a skyscraper. A 61-m-long steel cable of mass 38 kg
suspends the cabin. The man sends a signal to his colleague at the top of the
elevator shaft by tapping the cable with his hammer. How long will it take for
the wave pulse generated by the hammer to travel up the cable?(10%)
3.Determine the amplitude of the resultant wave when two sinusoidal string
waves having the same frequency and traveling in the same direction are
ocmbined, if their amplitudes are 6.0cm and 8.0 cm and they have phase
constans of 0 and π/2 rad, repectively(10%).(Hint: use Phasors)
4.please prove that
∞
∫ e^(-x^2)dx=√π/2
0
5.A satelltie is in a circular orbit around the Earth. The orbit has a radius
of 3.75 times the radius of the Earth. What is the linear speed of the
satellite?(10%). Hint: G=6.67x10^-11 m^3kg^(-1)s^(-2). The mass of the Earth
is 5.97x10^24 kg. The radius of the Earth is 6.37x10^6 m.
6.If you squeeze the handle of a spray bottle(Fig.1), you cause air to flow
horizontally across the opening of a tube that extends down into the liquid
almost to the bottom of the bottle. If the air is moving at 50.0m/s, what is
the pressure difference between the top of the tube ant the atmosphere? Assume
that the densityof air is ρ=1.20 kg/m^3 [Hint: Use Bernoulli's equatioin for
a negligible height difference. Before you squeeze the handle, the airflow
speed is zero.] (10%)
Figure 1 Spray bottle dor dispensing liquids in the form of a fine mist.
http://imgur.com/a/3olrO
7.Please find the general solution of the following equation:
d^2y dy
——-6—+9y=0 .(10%)
dx^2 dx
8.Let us conside n moles of an ideal gas doubles its volume in a free
expansion. Please use the Boltzmann's entropy equation S=klnW and Stirlings's
approximatioin lnN!=N(lnN)-N when N(the number of ideal gas moleclues) is
large to prove that Sf-Si=nRln2. [Hint:R is the gas constant, k=nR/N is the
Bltzmann constant, and W is the number of microstates]. (10%). Please prove
that if we use △S=∫dQ/T, the change of the entropy of an ideal gas doubles
its volume in a free expansion is also given by Sf-Si=nRln2. (10%)
9.Imagine a Carnot engine that operates between the temperatures TH=850K and
TL=300K. What is the efficiency of this engine? (10%) [Hint:fig.2]
Figure 2 The P-V diagram of a Carnot Engine.
http://imgur.com/ZZhogKI