複選題
25. Which of the following is a statement or a consequence of 2nd law of thermal dynamics?
(A) The efficiency of any heat engine operates between two heat reservoir is less or equal to the Carnot engine.
(B) Heat can never pass from a colder to a warmer body without some other changes occurring at the same time.
(C)Entropy of an object always increases when it is in contact with a heat reservoir.
(D) Isolated perpetual motion machine is not possible.
(E) The entropy of a thermal system going through a cyclic process always increases or stays the same after a full cycle.

1. If we denote the dimension of length as [L], dimension of time as [T], and dimension of mass as [M], what is the dimension of the universal gravitational constant G?(A) (B)(C)(D)(E)

2. A small ball of mass m is suspended in an elevator by a string of length L. The string does not stretch and its mass can be ignored. If the elevator located at the surface of the Earth and moves upward with an acceleration a, what is the frequency of the ball's oscillatory motion?(A) m(g - a)/(2πL), (B) m(g +a)/(2πL),(C)(D)(E)Here g is the gravitational acceleration on Earth's surface.

3. A block of mass 5 kg moving on a frictionless surface with a speed of 3 m/s collides with another block of mass 7 kg at rest. After the collision the two blocks stick together. What is the speed of the combined object?(A) 1.25 m/s, (B) 1.5 m/s, (C)1 m/s, (D) 0.5 m/s,(E) 2.0 m/s.

4. A satellite is on a circular orbit 3600km above ground. How much speed increase is needed for it to escape from Earth's gravity?(A) 11.2 km/s； (B) 3.3 km/s； (C)6.4 km/s； (D) 2.6 km/s； (E) 1.0 km/s.

5. A space craft is launched from the surface of the Earth with a heliocentric speed of 42 km/s (the speed relative to the Sun). What is its speed when it reaches a distance of 5 AU from the Sun? Note: you have to include the gravitational potential of the Earth as well as the Sun in the calculation.(A) 12 km/s； (B) 15km/s； (C)18 km/s； (D) 21 km/s； (E) 24km/s.

6. A solid spherical marble starts from rest and rolls without slipping on the loop-the-loop track in fgure 1. What is the minimum starting height h from which the marble will remain on the track through the loop. Assume the marbles radius is small compared with R. (A) 2.5R； (B) 2.7R； (C)2.9R； (D) 3.1R； (E) 3.3R. (Note: the moment of inertial for a solid spherical object is, where m is the mass of the object and r is its radius.) Figure 1: Figure for problem 6. Figure 2: Figure for problem 7.

7. What is the moment of inertia related to central axis A of a uniform solid pyramid of mass M and height h, with a square bottom of side L, as shown in figure 2. (A) 0.4MI3/h； (B) 0.2MLh； (C)0.1ML2, (D) 0.1MLh； (E) 0.2ML2.

8. A thin circular disk of radius R carries a total charge Q uniformly distributed on its surface. Assuming symmetric electric field on the two sides of the disk, which of the following expressions is a good approximation of the electric feld strength at a distance r above the center of the disk, where r << R?(A) (B) (C) (D)(E)

9. Same setting as in prablem 8, but with r ＞＞ R. Which of the following is a good approximation of the electric field strength?(A) (B) (C) (D) (E)

10. A piston system containing 1 mole of ideal gas in a 10 liter volume initially. The system is put in thermal contact with the environment at 20℃ and 1 atm of pressure. The piston is then released and the volume expands slowly in a quasi-static manner. The temperature is maintained at 20℃ during the whole process. The expansion stops when the pressure inside the piston reaches 1 atm. What is the volume of the gas chamber after the expansion? (The universal ideal gas constant, R, is 0.082 Liter-atm/K/mole.)(A) 24.1 liter； (B) 22.1 liter； (C)18.4 liter； (D) 16.9 liter； (E) 12.3 liter.

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