51. The diagram shows three isotherms for an ideal gas, with T₃-T₂ the same as T₂-T₁. It also shows five thermodynamic processes carried out on the gas. Rank the processes in order of the change in the internal energy of the gas, least to greatest.

(A) I, II, III, IV, V
(B) V； I； then III, and IV tied； then II
(C) I； then I, Ill and IV tied； then V
(D) II； I； then III, IV, and V tied
(E) V； then I, IIl and IV tied； then II

1. Two balls, projected at different times so they don't collide, have trajectories A and B, as shown below. Which statement is correct?(A) VOB must be greater than voA. (B) Ball A is in the air for a longer time than ball B. (C) Ball B is in the air for a longer time than ball A. (D) Ball B has a greater acceleration than ball A. (E) Ball A has a greater acceleration than ball B.

2.A shell explodes into two fragments, one fragment 25 times heavier than the other. If any gas from the explosion has negligible mass, then (A) the momentum change of the lighter fragment is 25 times as great as the momentum change of the heavier fragment. (B) the momentum change of the lighter fragment is exactly the same as the momentum change of the heavier fragment. (C) the momentum change of the heavier fragment is 25 times as great as the momentum change of the lighter fragment. (D) the kinetic energy change of the heavier fragment is 25 times as great as the kinetic energy change of the lighter fragment. (E) the kinetic energy change of the lighter fragment is 25 times as great as the kinetic energy change of the heavier fragment.

3.Two pure tones are sounded together and a particular beat frequency is heard. What happens to the beat frequency if the frequency of one of the tones is increased? (A)It increases. (B) It decreases. (C) It does not change. (D) It becomes zero. (E) We cannot tell from the information given.

4.When a fixed amount of ideal gas goes through an adiabatic expansion, A bar magnet is dropped from above and falls through the loop of wire shown below. The north pole of the bar magnet points downward towards the page as it falls. Which statement is correct? (A) The current in the loop always flows in a counterclockwise direction. (B) The current in the loop always flows in a clockwise direction. (C) The current in the loop flows first in a clockwise, then in a counterclockwise direction. (D) No current flows in the loop because both ends of the magnet move through the loop. (E) The current in the loop flows first in a counterclockwise, then in a clockwise direction.

5.A bar magnet is dropped from above and falls through the loop of wire shown below. The north pole of the bar magnet points downward towards the page as it falls. Which statement is correct? (A) The current in the loop always flows in a counterclockwise direction. (B) The current in the loop always flows in a clockwise direction. (C) The current in the loop flows first in a clockwise, then in a counterclockwise direction. (D) No current flows in the loop because both ends of the magnet move through the loop. (E) The current in the loop flows first in a counterclockwise, then in a clockwise direction.

6.A 3.0-kg mass is projected down a rough, circular track (radius =  2.0 m) as shown. The speed of the mass at point A is 4.0 m/s, and at point B, it is 7.0 m/s. What is the change in mechanical energydone on the system between A and B by the force of friction?(A) -24 J(B) -9.3 J(C) -8.1 J(D) -7.2 J(E) -6.6 J

7.A straight wire is bent into the shape shown. Determine the net magnetic force on the wire when the current I travels in the direction shown in the magnetic field B: (A) 2IBL in the +z direction (B) 2IBL in the -z direction (C) 4IBL in the +y direction (D)4IBL in the -y direction (E) zero

8.Three particles travel through a region of space where the magnetic field is out of the page, as shown in the figure. The electric charge of each of the three particles is, respectively, (A) 1 is positive, 2 is neutral, and 3 is negative (B) 1 is positive, 2 is negative, and 3 is neutral (C) 1 is neutral, 2 is negative, and 3 is positive (D) 1 is neutral, 2 is positive, and 3 is negative (E) 1 is negative, 2 is neutral, and 3 is positive

9.The figure shows the displacement y of a wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. Determine the frequency of the wave.  (A) 4.0 Hz (B) 3.0 Hz (C) 0.50 Hz (D) 0.33 Hz (E) 0.25 Hz

10. An ice cube at 0℃ is placed in a very large bathtub filled with water at 30℃ and allowed to melt, causing no appreciable change in the temperature of the bath water. Which one of the following statements is true? (A) The entropy gained by the ice cube is equal to the entropy lost by the water. (B) The entropy lost by the ice cube is equal to the entropy gained by the water. (C) The net entropy change of the system (ice plus water) is zero because no heat was added to the system. (D) The entropy of the system (ice plus water) increases because the process is irreversible. (E) The entropy of the water does not change because its temperature did not change.

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