Assumptions and Predictions of Kinetic Theory of Gases

To determine which statements are correct according to the Kinetic Theory of Gases (KTG), let us evaluate each option based on its fundamental postulates and predictions:

1. Option (A): Collisions are always elastic

   • Postulate of KTG: One of the core assumptions of the kinetic theory of gases is that collisions between gas molecules, as well as collisions between molecules and the walls of the container, are perfectly elastic.
   • Implication: There is no net loss of kinetic energy during collisions; kinetic energy is merely redistributed among the colliding molecules.
   • Therefore, Option (A) is correct.

2. Option (B): Heavier molecules transfer more momentum to the wall of the container

   • Analysis: The standard kinetic theory of gases treats a sample of a gas as consisting of identical molecules with a fixed mass $m$. The total pressure exerted by the gas depends on the total kinetic energy and the collision frequency rather than a comparison between molecules of different masses within the same gas. Thus, this statement is not a fundamental postulate or prediction of KTG.
   • Therefore, Option (B) is incorrect.

3. Option (C): Only a small number of molecules have very high velocity

   • Prediction of KTG (Maxwell-Boltzmann Distribution): The distribution of molecular speeds in a gas at temperature $T$ is given by the Maxwell-Boltzmann distribution law:
     $\frac{dN}{N} = 4\pi \left( \frac{m}{2\pi k_B T} \right)^{3/2} v^2 \exp\left(-\frac{mv^2}{2k_B T}\right) dv$
   • Analysis: As $v \to \infty$, the exponential term $\exp\left(-\frac{mv^2}{2k_B T}\right)$ dominates and rapidly approaches zero. Consequently, the fraction of molecules with very high velocities (as well as very low velocities) is extremely small, while most molecules possess speeds around the most probable speed $v_{\text{mp}} = \sqrt{\frac{2k_BT}{m}}$.
   • Therefore, Option (C) is correct.

4. Option (D): Between collisions, the molecules move in straight lines with constant velocities

   • Postulate of KTG: It is assumed that there are no attractive or repulsive intermolecular forces between ideal gas molecules except during actual physical contact (collisions).
   • Implication: In the absence of external forces and intermolecular forces, Newton's First Law of Motion implies that molecules travel in straight paths at constant speed between consecutive collisions.
   • Therefore, Option (D) is correct.

Conclusion

The correct options according to the kinetic theory of gases are (A), (C), and (D).