31. For an ideal gas in thermal equilibrium, which of the following statement is true?

(We define v_av, v_mp, and v_rms to be the average, the most probable, and the root-mean-square speeds of the gas respectively.)
(A) v_av ＜ v_mp ＜ v_rms
(B) v_mp ＜ v_av ＜ v_rms
(C) v_rms ＜ v_av ＜ v_mp
(D) v_rms ＜ v_mp ＜ v_av
(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.

38. An Ar-laser of λ = 540 nm is used to illuminate two slits of finite width a. The center-to-center distance between the slits is d. A diffraction pattern, shown in the figure, is observed on a screen 6.0 m away. The distance between two adjacent interference maxima is 3.0 mm. The values of d and a in units of mm are: (A) 0.27 and 0.14 (B) 0.54 and 0.14 (C) 1.08 and 0.54 (D) 1.08 and 0.27 (E) none of the above.

39. Linda uses a Michelson interferometer with the 606-nm light from a krypton-86 lamp and she places a gas cell of length 10.0 cm in the arm of movable mirror (as shown in the figure). Assuming the cell is filled with air at 1 atm which has an index of refraction n = 1.00025. Find the number of fringes moving across a line in her field of view if Linda slowly pumps out the air in the cell. (A) 413 (B) 41.3 (C) 165 (D) 16.5 (E) none of the above.

40. Which of the following functions represents traveling waves moving in the positive x direction? (A) Acos((kx + ωt)²) (B) Acos((kx)² - (ωt)²) (C) Asin(ωt)cos(kx) (D) Aexp(-(x - vt)²) (E) none of the above.

1. 關於校園霸凌事件處理,下列何者為非? (A) 關於疑似校園霸凌事件通報,對於當事人、檢舉人、證人及協助調查人之姓名或其他足以辨識其身分之資料,不論任何情況均應予以保密。 (B) 學校接獲檢舉,應初步了解是否為調查學校,並對學生啟動關懷輔導。 (C) 非調查學校接獲檢舉,知悉疑似校園霸凌事件時,除依規定通報外,應於三個工作日內將事件移送調查學校處理。 (D) 高級中等以下學校接獲前項檢舉,涉及疑似師對生霸凌事件,應移送學校校園事件處理會議處理。

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