42. Which of the following statements is true for one mole of ideal monatomic gases?
(A) For the isobaric process, the change in the internal energy is linearly proportional to the change in the temperature.
(B) For the gas undergoing the adiabatic process, the temperature of the gas remains constant.
(C) For the gas undergoing the isothermal expansion, the internal energy of the gas increases.
(D) For the gas undergoing the adiabatic free expansion process, the temperature of the gas drops.
(E) For the gas undergoing the adiabatic free expansion process, the internal energy of the gas increases.

38. For designing an anti-reflective coating for a glass surface in an optical device at a free-space wavelength of 552 nm. The refractive index of the glass is 1.50. Determine the minimum thickness (nm) of the optical coating with a refractive index of 1.38. (A) 276 (B) 184 (C) 138 (D) 100 (Ε) 92.0

39. A coin of mass m and radius R rolls steadily without slipping on a moving pad. Assume that the coin's face orientation remains fixed and its density is uniform. The coin rolls counter-clockwise and moves in the x-direction as shown in the figure. Suppose the pad is accelerating along the +x-direction with a constant acceleration a0 with respect to the inertial frame. What is the linear acceleration of the coin with respect to the inertial frame?  (A)+a0/3(B)-a0/3(C) +a0/2 (D) -a0/2 (E) 0 

40. What is the capacitance C of an isolated conductive spherical shell of radius R in free space with total charge Q uniformly distributed over its surface? (You can think of the second conductor as a hollow conducting shell of infinite radius.) (A) 0 (B) 4 πρ² Q (C) 2πε0RQ (D) 2 πε0Ρ (E) 4 πε0Ρ

41. A long, straight conductor carries 1.0 A of current. At what distance from the axis of the conductor is the magnetic field caused by the current equal to the Earth's magnetic field (about 0.5 Gauss)? μ0 = 4π × T·m/A (A) 200 mm (B) 40 mm (C) 20 mm (D) 4 mm (E) 1 mm

43. For a monatomic ideal gas undergoing the following three consecutive thermodynamic processes. First, an isochoric process from (P0, V0) to (2P0, V0). Second, an adiabatic free expansion from (2P0, V0) to (P0, 2V0). Finally, an isobaric process from (P0, 2V0) to (P0, V0). Which of the following statements is true? (A) The entropy of the gas and the entropy of the surroundings increase. (B) The entropy of the gas increases during the isochoric process. (C) The entropy of the gas increases during the isobaric process. (D) The entropy of the gas increases after one cycle is unknown since the gas undergoes the adiabatic free expansion process. (E) None of the above is true.

44. According to the Drude model, the speed of charge carriers driven in conducting media can be described by the concept of drift velocity under a bias voltage. Also, charge carriers (say, electrons) are used to be treated as free particles like ideal gas molecules that are thermally agitated into random motion with an average velocity . In common situations, what the estimated ratio (in the order of magnitude) of would be? (A) or even more (B) around 105(C) about 1(D) around   (E) or even less

45. For a sound wave travelling in a cylinder along the x-direction, a snapshot of the displacement field of air molecules is shown in the following figure. At which marked position, the sound wave possesses the largest energy density? The wave equation of sound is (A) The sound wave at A, C, and E all possess the largest energy density. (B) Only at point A since its amplitude is the largest. (C) Only at point C since it has the largest curvature. (D) The sound wave at B and E possess the largest energy density. (E) Only at point D since it has the largest slope.

46. Gold (Au) and tin (Sn) wires are joined together at both ends. The length ratio of the Au and Sn wires is 1:3 and both wires have the same cross-sectional area. A potential difference of Vis applied to the free ends. The ratio of the conductivities of Au and Sn is 5:1 and the ratio of the free electron densities of Au and Sn is 5:2. Which of the following statements is correct? Au Sn (A) The resistance of Au and Sn wires has the relation = 1:6. (B) The voltage across of Au and Sn wires has the relation = 1:15. (C) The electric field in Au and Sn wires has the relation = 1:1. (D) The drift velocity of electrons in Au and Sn wires has the relation =1:5. (E) None of the above is correct.

47. For a classical electromagnetic plane wave travelling in the x direction in a vacuum (with speed c), the electric field has the form = E0 cos(kx - wt) (V/m). Which of the following statements is true? (A) The magnetic field oscillates in the x direction with an amplitude | E0l/c (T). (B) The energy density of the electromagnetic wave is a constant everywhere in space. (C) The radiation pressure due to the electromagnetic wave shinning on a wall does not depend on its frequency. (D) The instantons power per unit area delivered by the electromagnetic wave is a constant. (E) None of the above is correct.

48. A bar magnet approaches a conducting loop from the left with its north pole directed towards the loop. Considering the effect of electromagnetic induction, the induced current in the loop has the greatest magnitude and a clockwise direction ________.(A) as the north pole of the magnet approaches the loop (B) when the north pole has passed through the loop, but the south pole has not yet passed through (C) when the north pole has passed through and the south pole is about to pass through the loop (D) as the south pole of the magnet leaves the loop (E) after the south pole of the magnet is several centimeters to the right of the loop