7. Continued from the last question, find the efficiency of this engine.

 (Note: adiabatic process of ideal gas: PVᵞ= constant, γ = C_p/C_v, C_v: molar specific heat at constant volume, C_p: molar specific heat at constant pressure.)

(A)

(B)

(C)

(D)

(E)

8. As shown in the right figure, a circuit is composed of a DC voltage source (V), two resistors (R₁ and R₂), one inductor (L), and a switch (S). Initially S is closed and the circuit is at steady condition, then S is opened at time t = 0. Find the current through the inductor as a function of time at t ＞ 0. (A)(B)(C)(D)(E)

9. A standing light wave is composed by two counter-propagating plane waves. The electric field is written as Estanding(r, t) = E₁(r, t) + E₂(r, t), where E₁(r, t) = E₀ cos(kz − ωt) ex and E₂(r, t) = E₀ cos(−kz − ωt) ex. Find the magnetic field of the standing wave.(A) B(r, t) = (2E₀/c) cos(kz) cos(ωt) ez(B) B(r, t) = (2E₀/c) cos(kz) cos(ωt) ey(C) B(r, t) = (2E₀/c) sin(kz) cos(ωt) ey(D) B(r, t) = (2E₀/c) cos(kz) sin(ωt) ey(E) B(r, t) = (2E₀/c) sin(kz) sin(ωt) ey

10. The setup of photoelectric effect experiment is shown in the following figure. The anode is irradiated by light with intensity I and frequency f. The electric potential between the anode and cathode is controlled by a variable power supply with voltage V. The resulted current A is measured by an ampere meter. If we use two difference light sources with the same intensity I and different frequencies f₁ and f₂, where f₁ ＜ f₂, which one of the following current-voltage (A-V) diagrams is correct?(A)(B)(C)(D)(E)

11. Consider the following optical phenomena, which ones of them can be deduced from Fermat's principle of least time?(A) single slit diffraction(B) double slit interference(C) reflection law (The angle of incidence is equal to the angle of reflection.)(D) refraction law (Snell's law)(E) zero reflection at Brewster's angle

12. Continued from the last question, which ones of them can be deduced from Maxwell's theory of electromagnetism?(A) single slit diffraction(B) double slit interference(C) reflection law (The angle of incidence is equal to the angle of reflection.)(D) refraction law (Snell's law)(E) zero reflection at Brewster's angle

13. Which ones of the following statements are the postulates of special relativity?(A) No object can moves with a speed higher than the speed of light in vacuum.(B) The speed of light in vacuum is the same in all inertial reference frames.(C) E = mc², where E is energy, m is mass, and c is speed of light in vacuum.(D) The space-time transformation obeys the Lorentz transformation.(E) All physical laws have the same form in all inertial reference frames.

14. In quantum mechanics, every dynamic variable is represented as an operator. Consider the position representation, which ones of the following statements are correct?(A) the momentum operator along x-axis is px = m (∂x/∂t)(B) the momentum operator along x-axis is px = −im (∂x/∂t)(C) the momentum operator along x-axis is px = −iℏ (∂/∂x)(D) the angular momentum operator is L = −iℏ (r × ∇)(E) the angular momentum operator is L = iℏ (∇× r)

15. Which ones of the following requirements are sufficient conditions for a ferromagnetic material?(A) The atoms of the material must have permanent magnetic dipole moment.(B) The atoms of the material must have no permanent magnetic dipole moment.(C) The atoms may or may not have permanent magnetic dipole moment.(D) There is no interaction between the atomic dipoles.(E) There are strong interactions between the atomic dipoles.

16. According to Planck's theory, which ones of the following quantities must be quantized to explain the spectrum of blackbody radiation?(A) spin of electrons(B) energy of electrons(C) momentum of electromagnetic waves(D) energy of electromagnetic waves(E) energy transfer between electromagnetic waves and electric oscillators

17. Consider the electromagnetic Poynting vector (S = E × H), which ones of the following statements are correct?(A) Poynting vector is the energy flux density of electromagnetic field.(B) Poynting vector is the momentum flux density of electromagnetic field.(C) Poynting vector is proportional to the momentum density of electromagnetic field.(D) Poynting vector is proportional to the angular momentum density of electromagnetic field.(E) Poynting vector is proportional to the optical pressure of an electromagnetic wave.

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