Chapter 13, Problem 16Q

To determine

To Explain: The concept of change in temperature and change in momentum of the molecules.

Explanation of Solution

Introduction:

According to the kinetic theory of the molecules, when the particles moves with the higher speed due to external effect from the surrounding. It leads to the high collision between the molecules.

According to kinetic energy, the velocity of the molecules with the temperature shows the following relation.

  $\mathrm{v}\propto \sqrt{\frac{3\mathrm{R}\mathrm{T}}{\mathrm{m}}}$

Here, $\mathrm{R}$ is the gas constant,

  $\mathrm{m}$ is the mass of the gas,

  $\mathrm{T}$ is the absolute temperature.

When a gas is pushed by the piston, the piston applies an external force on the gas molecules. Which increases their speed of the gas molecules. The increases in the speed also causes the increases in the collision between the molecules. When thee two gas molecules collides, they releases energy. This energy increases the temperature of the of the system. Similarly when the piston moves back, it causes reduction in the speed of the gas molecules. This causes the decrease in the temperature of gas molecules.

Conclusion:

Thus, momentum of the gas molecules is directly proportional to the temperature of the gas molecules. Increase in the velocity of the gas particles leads to increase in the temperature and vice-versa.