9. A 0.73 mole sample of hydrogen gas is at 400 K. According to the theoretical Maxwell-Boltzmann speed distribution, in thermal equilibrium, we can observe the most probable speed v_mp and average speed v_avg. Find the theoretical value of the ratio v_avg/v_mp. [The mass of a hydrogen atom is 1.67×10⁻²⁷ kg and the Boltzmann constant is 1.38×10⁻²³ J/K.]
(A) 1.13
(B) 1.41
(C) 1.57
(D) 1.73

1. A bottle contains oxygen gas. At 20°C, only translational and rotational motions of the oxygen molecules contribute to the specific heat. Cv and Cp are denoted as the molar specific heat at constant volume and pressure, respectively. Assume that the gas behaves like an ideal gas. What is the theoretical prediction Cp/Cv within the framework of the equipartition of energy? (A) 3/5 (B) 7/5 (C) 5/2 (D) 7/2.

2. The wave function of a propagating sinusoidal wave along x direction is generally written as the form y(x,t) = Asin(kx − ωt) What is the wave speed v? (A) v = (B) v = ωk (C) v = k/ω (D) v = ω/k

3. Consider an atom having energy levels labeled E1, E2, E3, .... The atom is in an excited state with an energy level E3, and it makes a transition back to a lower energy level E1. What is the frequency of the emitting photon? [h is denoted as the Planck constant] (A) (E3 − E1)/h (B) (E3 − E1)h (C) (E3 − E1)/h² (D) (E3 − E1)h³

4. An isolated charged capacitor of capacitance C0 has horizontal plates. A dielectric of dielectric constant K is inserted such that the capacitor is filled with the dielectric material. What is the resulting capacitance? (A) C0 (B) C0/K (C) KC0 (D) (K−1)C0

5. An isolated solenoid has self-inductance L0. A magnetic material of relative permeability Km is inserted in the solenoid such that it is filled with the magnetic material. What is the resulting self-inductance? (A) L0 (B) L0/Km (C) KmL0 (D) (Km−1)L0

6. The sound level is defined as β = 10log10(I/I0), where I0 = 1.00×10⁻¹² (W/m²). A point source emits sound waves with an average power output of 7.5×10⁻⁹ W. Calculate the sound level 10 meters from the source and the sound level 15 meters from the source. What is the difference in sound level (in decibels). (A) 0 (B) 2.44 (C) 3.52 (D) 4.79

7. The sound frequency of a train whistle is f = 450 Hz. Suppose that the speed of the train is u = 150 (km/hr) and the speed of sound is v = 343 (m/s). When the train approaches or recedes, the train whistle sounds higher or lower in frequency. Calculate the difference in frequency between the approaching and receding train whistle. (A) 151 Hz (B) 142 Hz (C) 130 Hz (D) 111Hz

8. Consider a piano string fixed at both ends. Its fundamental frequency is 470 Hz. The tension of the piano string is increased by 1.5 % and the mass density is unchanged. Find the new fundamental frequency. (A) 464 Hz (B) 473 Hz (C) 489 Hz (D) 492 Hz

10. The number of collisions a molecule makes per second is called collision frequency. At one atmosphere and 0 °C, estimate the collision frequency of air molecules. [The diameter of an air molecule under one atmosphere and 0 °C is approximately 3×10⁻¹⁰ (m), the average molecular speed is approximately 460 (m/s), and the molecular number density is approximately 2.7×10²⁵ molecules/m³]. (A) 3.5×10⁵ (collisions/s) (B) 3.5×10⁷ (collisions/s) (C) 3.5×10⁹ (collisions/s) (D) 3.5×10¹¹ (collisions/s)

11. Define the ratio of the specific heat γ = Cp/Cv, where Cp and Cv are the molar specific heat of an ideal gas at constant pressure and constant volume, respectively. A team of researchers measures the γ value of a new gas. Which of the following γ values is impossible? (A) 1.22 (B) 1.78 (C) 1.65 (D) 1.35

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