Concept explainers
Interpretation: The reason for gases to expand on heating and shrink on cooling needs to be explained.
Concept Introduction: The kinetic theory of gases is a simple
Answer to Problem 12E
Gases expand on heating and shrink on cooling due to an increase or decrease in the average kinetic energy of the gas particles upon heating or cooling.
Explanation of Solution
The
The mean free path of a gas is defined as the distance that a gas particle travels between successive collisions. When a sample of a gas is heated, the average kinetic energy of the gas increases. Thus, the average speed of the gas particles increases. As the average speed increases, the gas particles move more randomly and thereby the frequency of collisions decreases. Since fewer gas particles collide upon heating, the mean free path of the gas increases which leads to an increase in the volume of the gas.
The reverse is the situation on cooling of a gas. As the temperature of a sample of gas is lowered, the average kinetic energy decreases, thereby reducing the average speed. Thus, the particles move slowly and the frequency of collisions increases. Therefore, the mean free path and hence, the volume of the gas decreases.
Heating of a gas causes a volume increase due to the increase in average kinetic energy of the gas while cooling the gas leads to a decrease in the volume.
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