Chapter U3.60, Problem 2E

Interpretation Introduction

Interpretation: The reason for decrease in pressure of gas with decrease in temperature using kinetic theory has to be explained.

Concept introduction: Molecules of the gas are in constant motion. This motion leads to the pressure over the walls of the container.

Answer to Problem 2E

The pressure and temperature are directly related with each other at the conditions of constant volume and number of moles. Thus, due to this relationship decrease in temperature decreases the collision of the molecules and thus pressure decreases.

Explanation of Solution

According to Gay Lussac’s law, at the conditions of constant volume and constant number of particles, the relationship between pressure and temperature of gas is given as shown below.

  $P=\text{constant}\times T$

Thus, both pressure and temperature are directly proportional to each other. Now, when the gas temperature is increased then the kinetic energy of the molecules will also increase. This will lead to an increase in collision of molecules with the walls of the container. Thus, pressure exerted by gas molecules increases. Similarly, when temperature is decreased then the kinetic energy of particles will decrease. This will decrease their average speed. Hence, the collision with walls of the container decreases and ultimately the pressure will decrease.

Conclusion

The pressure and temperature are directly related with each other at the conditions of constant volume and number of moles. Thus, due to this relationship decrease in temperature decreases the collision of the molecules and thus pressure decreases.