45. During human respiration, oxygen passes through the alveoli (肺泡) into the bloodstream. Suppose an alveolus is approximated as a sphere with a volumn V = m³ and an internal pressure P = 1.2×10⁵ Pa. The oxygen content inside the alveolus is 25%. If air is treated as an ideal gas and the human body temperature is 37 °C (310 K), what is the number N oxygen molecules in a single alveolus? [Boltzmann constant k = J/K]
(A)
(B)
(C)
(D)
(E)

41. As shown in the Figure, a partition divides the space into two sections, A and B. The molar mass of the gas in section A is 14 g, while the molar mass of the gas in section B is 32 g. Assuming the total mass of the gases in A and B is the same, what is the ratio XA/XB of their lengths when equilibrium is reached? (A) 13/5 (B) 13/2 (C) 17/4 (D) 14/3 (E) 16/7

42. A parallel-plate capacitor has plates of area A = 8 m² and separation d = 1.5 mm. A dielectric sheet of the same area and thickness is placed between the plates. The dielectric constant is ɛ = 4.2. Determine the capacitance filled with the dielectric. [vacuum permittivity is ε0 = C/N·m²] (A)F (B)F (C)F (D) F (E)F

43. Suppose a coil has a magnetic dipole moment and is placed in a uniform magnetic field , where I and A are the current and area of the coil, respectively. What is the torque experienced by the coil? The vectors i,j,k are unit vectors corresponding to the x, y, and z axes, respectively. (A)(B) (C) (D) (E)

44. Two electric dipoles are placed horizontally along the x-axis, but one of them is oriented in the opposite direction, as shown in the Figure. Both electric dipoles have the same magnitude p. What is the electric potential V at point A on the z-axis at a distance L? (A)(B) (C)(D)(E)

46. The sound intensity level is defined as L = 10-log10(1/10) with the unit dB, where I is the sound intensity in units of W/m² and I0 = W/m². If a machine generates a noise level of 84 dB, what will be the noise level if an additional identical machine is turned on? [ = 0.301] (A) 84 dB (B) 168 dB (C) 90 dB (D) 190 dB (E) 87 dB

47. Two stars of masses M and 2M are in a binary star system, orbiting a common center of mass. Which of the following statements is true about their orbital periods? (A) The star with mass Mhas a longer orbital period. (B) The star with mass 2M has a longer orbital period. (C) Both stars have the same orbital period. (D) The orbital periods depend on the distance between the stars. (E) The orbital periods are independent of the masses of the stars.

48. A sample of gas is held in a container at a constant pressure. If the volume is halved, how will the rms (root-mean-square)-speed of the molecules change compared with the original rms-speed? (A) √2 times smaller (B) √2 times greater (C) the same (D) 2 times greater (E) 2 times smaller

49. A person with a volume of 0.08 m³ floats in fresh water (density = 1000 kg/m³). What is the buoyant force acting on the person? (Assume the acceleration due to gravity g is 10 m/s²) (A) 8000 N (B) 800 N (C) 80 N (D) 8 N (E) 0 N

50. A steam of water with a constant flow at 1 kg/s cools a machine. The water enters the machine at 10 °C and leaves at 80 °C. How much thermal energy is removed every minute? The specific heat capacity of water is 4.186 kJ/kg.K.(A) 17.6 MJ(B) 15.1 MJ(C) 251.2 kJ(D) 25.1 kJ(E) 2.5 MJ

51. A hot object at temperature 500 K is moved to contact with a cool object at 300 K, and a heat of 50 kJ flows irreversibly from one to the other. Assume that neighter object changes its temperature. How much is the entropy of the universe changed? (A) 1000 J/K (B) 40 MJ/K (C) 66.7 J/K (D) 62.5 J/K (E) none of the above