Question

Question: Describe what happens to the average kinetic energy of ideal gas molecules when the conditions are changed as follows:

(a) The pressure of the gas is increased by reducing the volume at constant temperature.

(b) The pressure of the gas is increased by increasing the temperature at constant volume.

(c) The average velocity of the molecules is increased by a factor of \({\rm{2}}\).

Short answer

(a) When the pressure of the gas is increased by reducing the volume at constant temperature, the average kinetic energy of ideal gas remains the same.

(b) When the pressure of the gas is increased by increasing the temperature at constant volume, the average kinetic energy of the ideal gas increases.

(c) When the average velocity of the molecules is increased by a factor of \({\rm{2}}\), the average kinetic energy of the ideal gas increases.

Step-by-step solution

Concept Introduction

The work that an object can accomplish as a result of its mobility is measured by its kinetic energy.

The average Kinetic Energy \(K{E_{avg}}\) is mathematically presented as:

\({\rm{K}}{{\rm{E}}_{{\rm{avg}}}}{\rm{ = }}\frac{{\rm{1}}}{{\rm{2}}}{\rm{mv}}_{{\rm{rms}}}^{\rm{2}}{\rm{ = }}\frac{{\rm{3}}}{{\rm{2}}}{\rm{RT,}}\)where m is the mass of the particle, v is the velocity of the particle, R is the universal gas constant, and T is the temperature.

Effect of Volume and Pressure

(a)

The average kinetic energy of a gas is directly proportional to the temperature and the changes in the temperature. It does not depend on pressure and volume. So, at a constant temperature, if the pressure and volume of a gas changes, the average kinetic energy does not change.

Therefore, the average kinetic energy remains the same.

Effect of Temperature and Pressure

(b)

The average kinetic energy of a gas is directly proportional to the temperature and the changes in the temperature. So, if the temperature of a gas increases, the average kinetic energy also increases.

Therefore, the average kinetic energy increases.

Effect of Velocity

(c)

Kinetic energy is proportional to the average velocity of a molecule. So, if the average velocity of the molecules is increased by a factor of \({\rm{2}}\), the average kinetic energy also increases.

Therefore, the average kinetic energy increases.