Kinetic Theory of Gases - Important Questions (WBCHSE Class 11)

Kinetic Theory of Gases

Important Questions for WBCHSE Class 11 Physics

Complete Study Guide with Formulas and Derivations

1

1-Mark Questions (VSA / MCQ)

• Define Mean Free Path of a gas molecule.
• What is the value of average velocity of gas molecules in thermal equilibrium?
• On which factor does the average Kinetic Energy of a gas depend?
• State the number of degrees of freedom for a monoatomic gas.
• Under what conditions of temperature and pressure does a real gas behave like an ideal gas?
• What is the total translational kinetic energy of 1 mole of an ideal gas at temperature T?
  \[E = \frac{3}{2}RT\]
• Define Absolute Zero temperature in terms of kinetic theory.

2

2-Mark Questions (Short Answer)

• State the Law of Equipartition of Energy.
• Why does the moon have no atmosphere? Explain based on rms speed.
• Deduce Boyle's Law from the kinetic theory of gases.
• Explain the kinetic interpretation of Temperature.
• State Graham's Law of Diffusion and write its mathematical form.
  \[\frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}}\]
• Calculate the ratio of \(v_{rms}\) to \(v_{av}\) for a gas at a given temperature.
  \[\frac{v_{rms}}{v_{av}} = \sqrt{\frac{3}{8/\pi}} \approx 1.085\]
• Define molar specific heat at constant volume (\(C_v\)) and constant pressure (\(C_p\)).

3-5

3 & 5-Mark Questions (Long Answer / Derivations)

• State the basic postulates/assumptions of the Kinetic Theory of Gases.
• Derive the expression for the pressure exerted by an ideal gas (\(P = \frac{1}{3} \rho \bar{v}^2\)).
  📝 Key Derivation Steps:

  1. Consider a gas molecule with velocity components \(v_x, v_y, v_z\)
  2. Change in momentum during collision with wall: \(2mv_x\)
  3. Force exerted = rate of change of momentum
  4. Pressure = Force/Area = \(\frac{1}{3} \rho \bar{v}^2\)

  Where \(\rho\) is density and \(\bar{v}^2\) is mean square speed.

• Using the law of equipartition of energy, calculate the ratio of specific heats (\(\gamma = C_p/C_v\)) for diatomic gases.
  📌 Important:

  For a diatomic gas at moderate temperatures:

  • Degrees of freedom = 5 (3 translational + 2 rotational)
  • \(C_v = \frac{5}{2}R\), \(C_p = C_v + R = \frac{7}{2}R\)
  • \(\gamma = \frac{C_p}{C_v} = \frac{7}{5} = 1.4\)
• Define and derive expressions for:

  1. Root Mean Square (rms) speed: \(v_{rms} = \sqrt{\frac{3kT}{m}} = \sqrt{\frac{3RT}{M}}\)
  2. Average speed: \(v_{av} = \sqrt{\frac{8kT}{\pi m}} = \sqrt{\frac{8RT}{\pi M}}\)
  3. Most Probable speed: \(v_{mp} = \sqrt{\frac{2kT}{m}} = \sqrt{\frac{2RT}{M}}\)
• Numerical: At what temperature will the rms speed of oxygen molecules be sufficient for escaping from the earth's atmosphere?

  Escape velocity from Earth: \(v_e = 11.2 \text{ km/s} = 11200 \text{ m/s}\)

  Using \(v_{rms} = \sqrt{\frac{3RT}{M}}\) and setting \(v_{rms} = v_e\):

  \[T = \frac{M v_e^2}{3R} = \frac{0.032 \times (11200)^2}{3 \times 8.314} \approx 1.6 \times 10^5 \text{ K}\]
• Numerical: A vessel contains a mixture of 2 moles of Hydrogen and 3 moles of Helium. Calculate the total internal energy of the system at temperature T.

  For Hydrogen (diatomic): \(U_H = 2 \times \frac{5}{2}RT = 5RT\)

  For Helium (monoatomic): \(U_{He} = 3 \times \frac{3}{2}RT = 4.5RT\)

  Total internal energy: \(U = U_H + U_{He} = 9.5RT\)

WBCHSE Class 11 Physics - Kinetic Theory of Gases

Complete Study Guide with Important Questions

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