7. 一容器內含 1 莫耳單原子理想氣體，已知在一絕熱過程中外界對氣體作功 7470 焦耳。若該氣 體的起始溫度為 200K、氣壓為 1.0×10⁴ 帕斯卡，則其最終氣壓為多少帕斯卡？ （氣體常數 R=8.3J/mole-K）

8. 一廣口容器與虹吸管裝置如右圖示，設虹吸管最高點 A 處截面積 a，而 下方出口 D 處截面積 2a，且容器截面積甚大於 a。若水無黏滯性、密度 d，A 高於容器水面 h、D 低於容器水面 h，重力加速度 g、大氣壓力 P。 則當虹吸管內水流正穩定自 D 處流出時，圖中 A 處之壓力為何？

9. 10.0 莫耳的理想氣體在溫度 T = 342 K 下，體積由 V 等溫(可逆)膨脹至 2V。求其熵的變化量 約為何？ (氣體常數 R=8.3J/mole-K)

10. 如圖，真空中有一玻璃製橢球體長軸 10cm、短軸 8cm，若 以平行於長軸之光線射向此橢球體，發現折射後的光線恰可通過橢球內的後方焦點上，則此玻璃之折射率為何？

1. As shown in Figure (1), space shuttle travels in a circular orbit 2R above the surface of the Earth with a period of T, where R is the radius of the Earth. The shuttle is now returning to the ground from point A of the orbit, it must reduce the speed at point A and enters a new elliptical orbit with the center of the Earth at one focus, and the orbit is tangent to the Earth's surface at point B. AB is the major axis of the ellipse. How long does it take for the shuttle to land from point A to the ground (point B)? In terms of T.

2. As shown in Figure (2), two identical blocks B and C of length 36.0 cm on the smooth horizontal surface, and the object A(treat A as a particle) is located at the right end of B, with the same mass of A, B and C. A and B are moving with the same speed toward the stationary C, and then B undergoes a one-dimensional completely inelastic collision with C. A is known to slide to the right end of C without falling and there is friction between A and C. Find the distance that C has traveled from the collision of B and C to A just arriving the right end of C.

3. Figure (3) shows the transverse velocity u versus time t of the point on a string at x = 0, as a wave passes through it. If the wave has the form y(x, t) = ym sin(kx - ωt - ϕ). What is the phase constant ϕ?

4. Pipe A has only one open end; pipe B is four times as long and has two open ends. Of the lowest 10 harmonic numbers nB of pipe B, what is the second smallest value at which a harmonic frequency of B matches one of the harmonic frequencies of A ?

5. A small lightbulb suspended at distance d1 = 250 cm above the surface of the water in a swimming pool where the water depth is d2 = 200 cm. The bottom of the pool is a large mirror. Looking down nearly perpendicularly, how far below the real mirror surface is the image of the bulb?

6. A particle of charge +Q is assumed to have a fixed position at P. A second particle of mass m and charge –Q moves at constant speed in a circle of radius R1, centered at P. Derive an expression for the work that must be done by an external agent on the second particle in order to increase the radius of the circle of motion, centered at P, to R2.

7. In Figure (4), a voltmeter of resistance Rv = 300 Ω and an ammeter of resistance RA = 5.00 Ω are being used to measure a resistance R in a circuit that also contains a resistance R0 = 100 Ω and an ideal battery of emf ε = 18.0 V. Resistance R is given by R = V/i, where V is the voltmeter reading and i is the current in resistance R. However, the ammeter reading is not i but rather i'. Thus, the ratio of the two meter readings is not R but only an apparent resistance R' = V/i'. Assume that R = 100 Ω. Calculate the apparent resistance R' ?

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