12. A Carnot engine operates between reservoirs at 500 K and 300 K. When it discharges 150 J to the lower-temperature reservoir, how much is the work done?
(A) 50 J
(B) 100 J
(C) 150 J
(D) 200 J
(E) 250 J

13. When an ideal gas undergoes an adiabatic free expansion, what remains unchanged during the process? (A) volume (B) temperature (C) pressure (D) entropy (E) density

14. Consider a large open tank with a small hole at its bottom. The tank is filled with water to a height of 1.25 m. What is the speed at which the water exits the tank through the hole? The acceleration of gravity is 10 m/s². (A) 1.25 m/s (B) 3.53 m/s (C) 5 m/s (D) 12.5 m/s (E) 25 m/s

15. An electric dipole with a dipole moment p is within a uniform electric field E. If the electric dipole is at an angle of 60° to the electric field, what is the external work needed to rotate the electric dipole to be perpendicular to the electric field? (A) pE (B) -pE (C)pE(D) -pE (E) (1-)pE

16. Consider a system consisting of a conducting sphere and a conducting spherical shell that are concentric. The radius of the sphere is a； the radii of the inner and outer surfaces of the shell are 2a and 3a, respectively, as shown in the figure. If the sphere carries a net charge of -Q and the shell carries a net charge of +2Q, what is the electric potential at a distance of a/2 from the center when the system is in electrostatic equilibrium? Assume that the zero of potential is at infinity. k is the Coulomb's constant. (A) -kQ/a (B) -2kQ/a (C) 2kQ/a (D) kQ/3a (E) -kQ/6a

17. The main reason for the generation of paramagnetism in materials is: (A) There is an effect of exchange coupling between electrons. (B) The magnetic dipoles of electrons tend to align with the applied magnetic field. (C) There are forces between the magnetic dipoles of electrons. (D) There are torques between the magnetic dipoles of electrons. (E) None of the above.

18. Consider the circuit in the figure, in which V = 30 V, R₁ = 10 Ω, R₂ = 15 Ω, R₃ = 30 Ω, and L = 20 mH. The switch is initially open. If the switch is closed for a long time and reopened, what is the voltage across R₂ when the switch is reopened?  (A) 7.5 V (B) 15 V (C) 22.5 V (D) 30 V (E) 45 V

19. Monochromatic light is normally incident on a diffraction grating that has 10000 slits and is 1 cm wide. If the second-order line is deviated at 30 degrees, what is the wavelength of the incident light? (A) 250 nm (B) 433 nm (C) 500 nm (D) 866 nm (E) 1000 nm

20. Consider a purely resistive heater connected to an AC power source (rms voltage 120 V, frequency 60 Hz) with an average heating power of 1 kW. If an inductor is connected in series with the heater, causing the average heating power to drop to 1/4 of its original value, what is the phase angle between the voltage and the current? (A) 15° (B) 30° (C) 45° (D) 60° (E) 90°

21. Consider an ideal parallel plate capacitor that is charged. If the capacitor plates are slightly pulled apart, which of the following statements is correct during the process? (A) The electric field strength inside the capacitor decreases. (B) The energy density inside the capacitor increases. (C) The potential difference between the capacitor plates remains unchanged. (D) The energy stored in the capacitor increases. (E) The capacitance of the capacitor increases.

22. For a hydrogen atom, the number of states in a shell with principal quantum number n is (A) n (B) 2n (C) 2n+1 (D) n² (E) 2n²

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