Chapter U3.53, Problem 11E

Interpretation Introduction

Interpretation: The properties of gas particles in a sample of gas need to be selected according to the postulates and assumptions of the kinetic molecular theory of gases.

Concept Introduction: The kinetic theory of gases is a simple thermodynamic model that aims to describe the macroscopic properties of gases like the pressure, temperature, etc in terms of microscopic parameters like the speed of the gas particles. The kinetic theory is based on a number of postulates concerning the size and the random motion of the gas particles in a sample and the derivations from the kinetic theory are approximate at best.

Answer to Problem 11E

The correct answer is the second option, option (B).

Explanation of Solution

Reason for correct option: The ideal gas law is governed by the kinetic theory of gases. The kinetic theory of gases is based on the following assumptions about the gas particles.

(i) A gas is composed of hard spherical particles that are in constant random motion.

(ii) The gas particles are massless spheres, i.e., they exert no force.

(iii) The gas particles are assumed to be infinitely small such that the volume of the gas particles is negligible compared to the volume of the gas. In fact, the volume of the gas is mainly due to the free space or the distance between the gas particles.

(iv) The gas particles move about in straight lines and collide with each other or the walls of the container. These collisions are assumed to be perfectly elastic, that is there is no energy loss when the gas particles collide with each other or with the walls. Hence, there is conservation of energy during these collisions.

(v) The gas particles have random speeds or velocities (the directions change depending on the collisions), but the average kinetic energy of the gas particles depends only on the temperature of the gas. In fact, the average kinetic energy and thus, the average speed of a sample of gas particles is only a function of the absolute temperature of the gas.

Conclusion

Reason for incorrect options: The first option, option (A) is incorrect because the gas particles move about in straight line paths and collide with each other as well as the walls of the container. The third option, (C) is incorrect because the gas particles have different speeds, but the same average kinetic energy that depends only on the absolute temperature of the gas. Since options (A) and (C) are incorrect, option (D) is automatically incorrect.