課程名稱︰普通物理學甲下
課程性質︰系必修
課程教師︰張寶棣
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰104/3/31
考試時限（分鐘）：120
試題 :
1. Please answer the following questions.
‧What is equipartition principle? Why is the latent heat of vaporization
for water so much larger than the latent heat of fusion?
‧Explain why entropy in an isolated system must reach its maximum.
Biological system use energy (ultimately from the Sun) in organizing
highly ordered organisms, such as humans. Does this mean that biological
system violate the second law of thermodynamics? Explain your answer.
‧Describe the Gauss's Law. If our space is four dimensional, what will
you expect the r dependence of the coulomb's law?
2. The inside of a hollow cylinder is maintained at a temperature T_a while
the outside is at a lower temperature, T_b. The wall the cylinder has a
thermal conductivity κ. Ignoring end effects, show that the rate of
energy conduction from inner to the outer surface in the radial direction
is dQ/dt = 2πLκ[(T_a-T_b)/ln(b/a)].
(Hint: In a steady flow dQ/dt is a constant. The temperature gradient
is dT/dr and the surface area A at radius r is 2πrL.)
3. The diesel cycle shown in Fig. approximates the behavior of a diesel
engine. Process ab is an adiabatic compression, process bc is an expansion
of costant pressure, process cd is an adiabatic expansion, and da is a
cooling at constant volume. Find the efficiency of this cycle in terms
of volumes, V_a, V_b, V_c, and V_d.
　
Ｐ｜ Costant pressure
　｜ expansion
　｜ｂ　　ｃ
　｜．-→-．
　｜｜　　 \ Adiabatic
　｜ \ ↘ expansion
　｜ \　　　‵*-．ｄ
　｜　 ＼ 　　　 ｜ Costant
　｜ ↖ 　　 ↓ volume cooling
　｜　 ︿ ｜
　｜ ‵*-．ａ
　｜ Adiabatic
　｜ compression
　∟＿＿＿＿＿＿＿＿＿＿＿＿
　　　　　　　　　　　　　Ｖ
Fig.
4. The combustion of acetylene is represented by the chemical reaction
2(C2H2)+5(O2)→4(CO2)+2(H20). The amount of energy released in the
combustion of one mole of acetylene is 300 kcal. One mole of acetylene
and 2.5 moles of oxygen at 300K are confined in an insulated enclosure
at a pressure of 1 atm. (a) Find the temperature and volume following
combustion if pressure is maintained at 1 atm. (b) If, following
combustion, the thermal insulation about the container is removed and
the system is cooled at 300 K, what is the final pressure?
5. A mole of a monatomic ideal gas is taken from an initial pressure p and
volume V to a final pressure 3p and 3V by two different processes:
(I) It expands isothermally until its volume is tripled, and then its
pressure is increased at costant volume to the final pressure.
(II) It is compressed isothermally until its pressure is tripled, and
then its volume is increased at costant pressure to the final volume.
Show the path of each process on a p－V diagram, for each process
calculate, in terms of p and V, (a) the heat absorbed by the gas in each
part of the process, (b) the work done by the gas in each part of the
process, (c) the change in internal energy of the gas, U_int,f - U_int,i,
and (d) the change in entropy of the gas, S_f - S_i.
6. The charge density in a region of space of spherically symmetric and is
given by ρ(r) = C*e^(-r/a) when r<R and ρ=0 when r>R. Find the electric
field as a function of r.
7. A metal sphere of radius a is surrounded by a metal shell of inner radius
b and outer radius R. The flux through a spherical Gaussian surface located
between a and b is Q/ε_0, and the flux through a spherical Gaussian
surface just outside radius R is 2Q/ε_0. What are the total charges on
the inner sphere and on the shell? Where are the charges located, and
what are the inner charge densities?