課程名稱︰普通物理學甲下 課程性質︰化學系大一必修 地質系選修 課程教師︰張寶棣 開課學院：理學院 開課系所︰物理系 考試日期（年月日）︰2017/04/06 考試時限（分鐘）：120 分鐘 試題 : 1. Please answer the following questions. (a) You have a container of a dilute gas at a certain temperature and inject a small quantity of a different type of molecule into that container. What processes determine how long it takes the new molecules to come to thermal equllibrium with the original molecules? (5%) (b) 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 biolog- ical system violate the second law of thermodynamics? Explain your answer. (5%) (c) Atoms consist of negatively charged electrons bound to the positively charged nucleus by the Coulunb force. The electrons are rearranged when two different chemicals are brought together. Would you expect the electrons that are closer to the nucleus or the ones that are farther from the nucleus to be more involved in chemical reactions? (5%) 2. A cylinder of closed at both ends and has insulating walls. It is divided into two compartments by a perfectly insulating partition that is perpen- dicular to the axis of the cylinder. Each compartment contains 1.00 mol of oxgen, which behaves as an ideal gas with γ= 1.4. Initially the two compartments have equal volumes, and their temperatures are 550K and 250K. The partition is allowed to move slowly until the pressures on its two sides are equal. (a) Find the work done by the gas in the two compartme- nts. (b) Find the final temperatures in the two compartments. (Hints: You need to use the condition of adiabatic process: PV^γ= const., and dE_int = -PdV (15%) 3. 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 combu- stion of one mole of acetylene is 300 kcal. One mole of acetylene and 2.5 moles of oxygen at 300 K are confined in an insulated enclosure at a pre- ssure of 1 atm. (a) Find the temperature and volume following combustion if pressure is maintained at 1 atm. (b) If following combustion, the the- rmal insulation about the container is removed and the system is cooled at 300 K, what is the final pressure? (15%) 4. 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 pressu- re is increased at constant volume to the final pressure. (II) It is co- mpressed isothermally until its pressure is tripled , and then its volume is increased at constant pressure to the final volume. Show the path of each process on a p-V diagram. For each process caculate, 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 entr- opy of the gas, S_f-S_i. (20%) 5. The charge density in a region of space of spherically symmetric and is given by ρ= Ce^(-r/a) when r < R and ρ= 0 when r > R. Find the electric field as a function of r. (10%) 6. A molecule of lithium fluoride (LiF) has a permanent dipole moment. The molecule is placed in a uniform electric field of strength 10^4 N/C, and the difference between the maximum and the minimum potential energies of the molecule in this field is 4.4×10^(-25) J. What is the electric dip- ole moment of the LiF molecule? (10%) 7. The inside of a hollow cylinder is maintained at a temperature T_a while the outside is at a lower temperature, T_b (see Fig. 1) The wall the cyl- inder has a thermal conductivity κ. Igonring the 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 surf- ace area A at radius r is 2πrL. (15%) Fig. 1 http://imgur.com/c9ts7Qm --

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