二、問答計算題(共70分） 

1.在推導氣體動力論巨觀現象與微觀行為關係式時，我們常用正立方體密閉容器當 例子。若有學生詢問其他形狀密閉容器是否適用相同關係式，你會如何回答並舉 例推導說明？（5%)

1. In physics, the Planck length is a unit of length. It is developed by physicist Max Planck. The Planck length can be defined from three fundamental physical constants: the speed of light in vacuum c, the Planck constant h, and the gravitational constant G. Please use the dimensional analysis to derive the Planck length from c, h, and G.

2. Water is moving with a speed of 4 m/s through a pipe with a cross-sectional area of 5 cm2. The water gradually descend 10 m as the pipe increases in area to 10 cm2. If the pressure at the upper level is 1.5 x105 Pa, what is the pressure at the lower level? (g=10 m/s2)

3. The temperature of 2.00 mol of hydrogen gas is raised 40.0 K at constant volume. The molecules in the gas rotate but do not oscillate. How much energy is transferred to the gas as heat Q?

4. Two waves are generated on a string of length 3.0 m to produce a three-loop standing wave with an amplitude of 1.0 cm. The wave speed is 100 m/s. Let the equation for one of the waves be of the form y(x,t) = ym sin(kx + ωt). In the equation for the other wave, what are (1) k, and (2) ω?

5. An ambulance with a siren emitting a whine at 1710 Hz overtakes and passes a cyclist pedaling a bike at 10 m/s. After being passed, the cyclist hears a frequency of 1575 Hz. How fast is the ambulance moving? (the speed of sound in air is 340 m/s)

6. A thin flake of mica(n = 1.58) is used to cover one slit of a double-slit arrangement. The central point on the screen is occupied by what used to be the seventh bright fringe. If A = 6380 Å(in vacuum), what is the thickness of the mica?

7. The electric field in a region of space has the components Ey = Ez = Q and Ex = 4.00x (N/C). Point A is on thej; axis at y = 3.00 m, and point B is on the x axis at x = 4.00 m. What is the potential difference VB - VA?

8. Three charges of +0.1 C each are placed on the corners of an equilateral triangle, 1.0 m on a side. If energy is supplied at the rate of 1.0 KW, how many hours would be required to move one of the charges onto the midpoint of the line joining the other two?

9. Figure 1 shows a wood cylinder of mass m = 0.25 kg and length L =0.10 m, with N = 10 turns of wire wrapped around it longitudinally, so that the plane of the wire coil contains the long central axis of the cylinder. The cylinder is released on a plane inclined at an angle 6 to the horizontal, with the plane of the coil parallel to the incline plane. If there is a vertical uniform magnetic field of magnitude B = 0.50 T, what is the least current I through the coil that keeps the cylinder from rolling down the plane?

10. A stationary, circular wall clock has a face with a radius of 20 cm. Six turns of wire are wound around its perimeter; the wire carries a current 2.0 Ain the clockwise sense. The clock is located where there is a constant, uniform external magnetic field of 50 mT(but the clock still keeps perfect time). At exactly 1:00 p.m., the hour hand of the clock points in the direction of the external magnetic field. After how many minutes will the minute hand point in the direction of the torque on the winding due to the magnetic field?

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