45. A cube of metal has an edge length of 10 cm. It has a density 3.0 g/cm³ and a specific heat 0.2cal/g°C. When the internal energy of the cube increases by 9000 cal, its temperature increases by _____.
(A) 9°C
(B) 10°C
(C) 12°C
(D) 15°C
(E) 20°C

41. The human ear canal is, on average, 2.5 cm long. ft is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range)of the standing waves in the ear canal. Recall that, at 20C, the speed of sound in air is about 343 m/s.(A) 1715 Hz (B) 3430 Hz (C) 6860 Hz (D) 13720 Hz (E) 20580 Hz

42. The charge Q is -3.0 nC. How much charge q1 is needed to bringcharge q2 into static equilibrium?(A) -6 nC (B) 6 nC (C) 3 nC (D) 12 nC (E) -12 nC

43. A rectangular coil of N turns, each of width α and length b is in amagnetic field B directed into the page, with only half of the coil in theregion of the magnetic field. The resistance of the coil is R. The coil canbe moved to the right, up or down. What is the magnitude of the inducedcurrent if the coil is moved with a speed v down?(A) 4NBav/R (B) NBav/R (C) 2NBav/R (D) 2NBav (E)NBav/R

44. The surface water temperature in tropical oceans is above 25℃, and the deep-water temperature is about 4°C. If the Carnot engine is operated at these two temperatures, what is the maximum efficiency of this engine?(A) 7 % (B) 9 % (C) 16 % (D) 84 % (E) 93 %

46. Sound pressure level is defined as SPL(dB) = (P⁄P0), where P is sound wave pressureand P0 = 20 μPa. SPL decreases 6 dB as a listener's distance doubles from the sound source. Thesound level is 110 dB at one meter away from the explosion of firecrackers. How far away wouldit be needed to reduce the sound level to an acceptable level of 80 decibels?(A) 5 m (B) 16 m (C) 32 m (D) 60 m (E) 100 m

47. A 5.0 L gas tank holds 1.7 mole of monoatomic helium (He) and 1.1 mole of diatomic oxygen (O2), at a temperature of 260 K. The atomic masses of helium and oxygen are 4.0 g/mol and 16.0 g/mol, respectively. What is the ratio of the root-mean-square (thermal) speed of helium to that of oxygen?(A) 1.4 (B) 2.0 (C) 2.8 (D) 4.0 (E) 5.6

48. A piece of thin uniform wire of mass m and length 3b is bent into an equilateral triangle. Find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices.(A)(B) (C) (D)(E)

49. One way to measure blood flow when blood vessels are exposed during surgery is to use anelectromagnetic flowmeter. The device surrounds the blood vessel with an electromagnet tocreate a magnetic field perpendicular to the blood flow. Since blood is a modest conductor, amotional emf develops across the blood vessel. Given the vessel diameter d, magnetic field B,and voltage V measured across the vessel, what is the volume flow rate of blood?(A) πdV⁄(4B) (B) πdV⁄(2B) (C) πdV⁄B (D) 2πdV⁄B (E) 4πdV⁄B

50. Suppose that 1 mole of an ideal gas undergoes a free expansion to three times its initial volume.What is the change of entropy? (The universal gas constant is R.)(A) 2R ln 2 (B) R ln 2 (C) R ln 3 (D) R ln 4 (E) 2R ln 4

51. A proton of mass m and charge q is in uniform circular motion perpendicular to a magnetic fieldB . The radius of the circle is r. What is the speed of the proton?(A) qBr/3m (B) 2qBr2/(2m(r + 1)) (C) qBr2/(2m(r + 1))(D) qBr/2m (E) qBr/m