RMS speed, degrees of freedom and equipartition - Question Bank

1. If the temperature of a gas is increased, the collision frequency of the molecules:
A) Increases
B) Decreases
C) Remains constant
D) Becomes zero
2. The number of degrees of freedom for translational motion is always:
A) 3
B) 2
C) 1
D) 5
3. For a monatomic gas, Cp - Cv = R. For a diatomic gas, Cp - Cv is also R. This is an application of:
A) Mayer's relation
B) Ideal gas law
C) Dalton's law
D) Avogadro's law
4. The equipartition theorem applies to systems in:
A) Thermal equilibrium
B) Mechanical equilibrium
C) Chemical equilibrium
D) Phase equilibrium
5. Which gas will have the lowest RMS speed at 27°C?
A) Helium (He)
B) Neon (Ne)
C) Argon (Ar)
D) Krypton (Kr)
6. The average kinetic energy of a diatomic molecule at temperature T is approximately:
A) 5/2 kT
B) 3/2 kT
C) kT
D) 7/2 kT
7. At absolute zero temperature, the RMS speed of gas molecules is:
A) Zero
B) Minimum
C) Maximum
D) Undefined
8. In the equation v_rms = sqrt(3kT/m), what does 'm' represent?
A) Mass of a single molecule
B) Molar mass
C) Boltzmann constant
D) Universal gas constant
9. The internal energy of an ideal gas depends only on:
A) Temperature
B) Pressure
C) Volume
D) Number of moles
10. A non-linear triatomic molecule has how many degrees of freedom at moderate temperatures?
A) 6
B) 5
C) 7
D) 9
11. Which statement is incorrect regarding the RMS speed of gas molecules?
A) It increases with temperature.
B) It decreases with increasing molar mass.
C) It is directly proportional to the pressure.
D) It is proportional to the square root of temperature.
12. The equipartition theorem is a consequence of:
A) Classical mechanics
B) Quantum mechanics
C) Relativistic mechanics
D) Thermodynamics
13. If the volume of a gas is kept constant, and its temperature is increased, the RMS speed of the molecules:
A) Increases
B) Decreases
C) Remains constant
D) Becomes zero
14. For a monatomic gas, the internal energy per mole is:
A) 3/2 RT
B) 5/2 RT
C) 7/2 RT
D) RT
15. The specific heat capacity of a gas depends on:
A) Degrees of freedom
B) Molecular weight
C) Temperature
D) Pressure
16. The adiabatic process is described by PV^γ = constant. What does γ represent?
A) Ratio of specific heats (Cp/Cv)
B) Ratio of molar masses
C) Ratio of absolute temperatures
D) Ratio of pressures
17. A triatomic linear molecule (like CO2) has how many degrees of freedom related to vibration?
A) 1
B) 2
C) 3
D) 4
18. The mean free path of gas molecules depends on:
A) Temperature and pressure
B) Molecular diameter and number density
C) Volume and number of moles
D) RMS speed and temperature
19. If the pressure of an ideal gas is doubled while keeping the temperature constant, the RMS speed of its molecules will:
A) Remain unchanged
B) Double
C) Halve
D) Increase by a factor of sqrt(2)
20. What is the value of the universal gas constant (R)?
A) 8.314 J/mol·K
B) 1.38 x 10^-23 J/K
C) 6.022 x 10^23 mol^-1
D) 9.8 m/s²
21. For a rigid diatomic molecule, rotational degrees of freedom contribute:
A) kT
B) 1/2 kT
C) 3/2 kT
D) 2 kT
22. The average energy of a photon in black body radiation is given by kT. This is an example of:
A) Equipartition theorem
B) Maxwell-Boltzmann distribution
C) Ideal gas law
D) Dalton's law
23. If the temperature of a gas is increased by 2 K, the increase in its average kinetic energy per molecule is:
A) 2k
B) 3/2 k
C) 3k
D) 3/2 R
24. The average translational kinetic energy of gas molecules is directly proportional to:
A) Absolute temperature
B) Pressure
C) Volume
D) Density
25. Which type of gas molecule has the maximum number of degrees of freedom at room temperature among monatomic, diatomic, and triatomic (linear)?
A) Monatomic
B) Diatomic
C) Triatomic (linear)
D) All have the same
26. The RMS speed of gas molecules is independent of:
A) Temperature
B) Molar mass
C) Number of molecules
D) Universal gas constant
27. At higher temperatures, the contribution of vibrational modes to the specific heat of a diatomic gas becomes significant. This leads to:
A) An increase in Cv
B) A decrease in Cv
C) No change in Cv
D) An increase in Cp
28. If a gas has f degrees of freedom, its molar specific heat at constant volume is given by:
A) f/2 R
B) f R
C) (f+1)/2 R
D) (f+2)/2 R
29. For a diatomic molecule, vibrational degrees of freedom contribute how much energy per molecule according to equipartition theorem?
A) kT
B) 1/2 kT
C) 3/2 kT
D) 2 kT
30. The equipartition theorem is applicable under which condition?
A) Thermal equilibrium
B) High pressure
C) Low temperature
D) Non-ideal conditions
31. Which of the following is NOT a degree of freedom for a molecule?
A) Translational motion
B) Rotational motion
C) Vibrational motion
D) Intermolecular attractive force
32. The ratio of specific heats (Cp/Cv) for a diatomic ideal gas at moderate temperatures is approximately:
A) 1.40
B) 1.67
C) 1.33
D) 1.20
33. The ratio of specific heats (Cp/Cv) for a monatomic ideal gas is known as the adiabatic index, γ. What is its value?
A) 1.67
B) 1.40
C) 1.33
D) 1.20
34. What is the specific heat at constant volume (Cv) for a diatomic ideal gas per mole at moderate temperatures?
A) 5/2 R
B) 3/2 R
C) 7/2 R
D) 9/2 R
35. What is the specific heat at constant volume (Cv) for a monatomic ideal gas per mole?
A) 3/2 R
B) 5/2 R
C) 7/2 R
D) R
36. For a diatomic molecule in thermal equilibrium, the total average internal energy per molecule is:
A) 5/2 kT
B) 3/2 kT
C) 7/2 kT
D) 9/2 kT
37. According to the equipartition theorem, the average energy associated with translational motion for a molecule is:
A) 3/2 kT
B) kT
C) 5/2 kT
D) 7/2 kT
38. What does the equipartition theorem state?
A) Each degree of freedom of a molecule contributes 1/2 kT to its average energy
B) Each degree of freedom contributes kT to its average energy
C) Each degree of freedom contributes 3/2 kT to its average energy
D) The total energy is equally distributed among all molecules
39. At very high temperatures, a diatomic molecule can have how many degrees of freedom?
A) 5
B) 6
C) 7
D) 9
40. A diatomic molecule typically has how many degrees of freedom at moderate temperatures?
A) 3
B) 4
C) 5
D) 6
41. For a monatomic gas molecule, what is the number of degrees of freedom?
A) 1
B) 2
C) 3
D) 5
42. What is meant by the 'degrees of freedom' of a molecule?
A) The number of ways a molecule can move
B) The number of atoms in a molecule
C) The number of bonds in a molecule
D) The number of collisions a molecule makes
43. Which of the following gases will have the highest RMS speed at a given temperature?
A) Oxygen (O2)
B) Nitrogen (N2)
C) Hydrogen (H2)
D) Carbon Dioxide (CO2)
44. The ratio of RMS speed of hydrogen molecules to that of oxygen molecules at the same temperature is:
A) 4:1
B) 1:4
C) 2:1
D) 1:2
45. What is the average kinetic energy of one molecule of an ideal gas at absolute temperature T?
A) 3/2 kT
B) kT
C) 3/2 RT
D) RT
46. The kinetic energy of a gas is directly proportional to:
A) Absolute temperature
B) Pressure
C) Volume
D) Number of moles
47. What is the unit of Boltzmann constant (k)?
A) Joule per Kelvin (J/K)
B) Joule per mole Kelvin (J/mol·K)
C) Pascal meter cubed per Kelvin (Pa·m³/K)
D) Watt per Kelvin (W/K)
48. If the absolute temperature of a gas is doubled, how does its RMS speed change?
A) It increases by a factor of sqrt(2)
B) It doubles
C) It increases by a factor of 4
D) It remains the same
49. In the formula for RMS speed, v_rms = sqrt(3RT/M), what does 'M' represent?
A) Mass of a single molecule
B) Molar mass of the gas
C) Boltzmann constant
D) Universal gas constant
50. The RMS speed of gas molecules is given by the formula:
A) v_rms = sqrt(3RT/M)
B) v_rms = sqrt(RT/M)
C) v_rms = sqrt(3kT/m)
D) v_rms = sqrt(kT/m)
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