27. A coil with N₁ turns and radius R is placed around a very long solenoid with cross section S and N₂ turns. The windings of the solenoid have length L. What is the mutual inductance of the system?

(A)
(B)
(C)
(D) μ₀SN₁N₂
(E)

28. A cylindrical container of an incompressible liquid with density ρ rotates with constant angular speed ω about its axis of symmetry, which we take to be the y-axis. The gravitational acceleration is g. The surface height h of the liquid is given by: (A) ω²r²/2g (B) ω²r²/g (C) ω²r²/2gρ (D) ω²r²/gρ (E) none of the above.

29. After going through a free expansion, the temperature of a real gas whose intermolecular interaction is an attractive force would (A) remain the same (B) increase (C) decrease (D) not be definable (E) be arbitrary.

30. For an infinitesimal reversible process of a thermodynamic system, which of the following statement is not true? (A) dU = CvdT - pdV (B) dU = TdS - pdV (C) dS ＞ 0 (D) There can not be any frictional force. (E) there is no heat exchange between the system and an thermal bath with a finite temperature difference.

31. For an ideal gas in thermal equilibrium, which of the following statement is true? (We define vav, vmp, and vrms to be the average, the most probable, and the root-mean-square speeds of the gas respectively.) (A) vav ＜ vmp ＜ vrms (B) vmp ＜ vav ＜ vrms (C) vrms ＜ vav ＜ vmp (D) vrms ＜ vmp ＜ vav (E) None of the above. 

32. A volume of air (assumed to be an ideal gas) undergoes the thermodynamic process, as shown by the path abc in the figure. What is the ratio of Tc to Ta? How much heat does the air exchange with its surroundings during the process abc? The answers to these two questions are: (A) 1.0 and 8.0 kJ (B) 1.0 and 4.0 kJ (C) 3.0 and 8.0 kJ (D) 3.0 and 4.0 kJ (E) none of the above.

33. A thermally insulated chamber has two equal-volume compartments with a movable insulated partition in between. Initially one compartment contains two moles of helium gas at T = 100 K, and the other compartment contains one mole of argon gas at T = 400 K. Assume that both gases can be considered ideal gas. What is the total change of entropy of the system after the compartment has been removed and the gases have reached a new equilibrium? (A) 1.5Rln2 (B) 3Rln2 (C) 4.5Rln2 (D) 6Rln2 (E) none of the above.

34. The speed of sound in a stationary air is 340 m/s. A police car with its 300-Hz siren turned on is moving toward a wall at 180 km/hour. The frequency of the reflected wave that the driver of the car hear is: (A) 403 Hz (B) 223 Hz (C) 344 Hz (D) 351 Hz (E) none of the above.

35. A police uses a radar gun of frequency f₀ to measure an approaching car moving at a speed of v. The frequency of the reflected beam measured by the police is: (A) (B) (C) f₀(c-v)/(c+v) (D) f₀(c+v)/(c-v) (E) none of the above.

36. A plane wave of monochromatic light is incident on an opaque metal sheet with four equally-spaced narrow slits. If the incident angle is slanted so that φ = nπ/2 is the phase difference between adjacent slits, and n is an integer. The center line at a far away screen parallel to the sheet is: (A) a bright line (B) a dark line (C) half way between a bright line and a dark line (D) a major bright line if n is a multiple of 4 and a minor bright line otherwise (E) a bright line if n is a multiple of 4 and a dark line otherwise.

37. Slits of unequal widths are used in a double-slit arrangement to produce an interference pattern on a distant screen. If only the narrower slit S₁ is illuminated with monochromatic light of wavelength λ, the center of the pattern on the screen has amplitude E₀ and intensity I₀. If only the wider slit S₂ is illuminated, the amplitude of the light at the center of the pattern is 2E₀. In the figure on the right, d ＜＜ D. The widths of the slits are much less than λ such that it is no need to consider the single-slit diffraction envelope. When both slits are illuminated, the normalized intensity pattern I(θ)/I₀ as a function of θ on a far away screen is: (A) (5 + 4cos(2πd sinθ/λ)) (B) (4 + 5cos(2πd sinθ/λ)) (C) (3 + 2cos(2πd sinθ/λ)) (D) (2 + 3cos(2πd sinθ/λ)) (E) none of the above.

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