Understanding Boyle's Law: The Effect of Volume Increase at Constant Temperature

[bobsmith76]

Effect of a volume increase at constant temperature: A constant temperature means that the average kinetic energy of the gas molecules remains unchanged. This in turn means that the rms speed of the molecules, u, is unchanged. If the volume is increased, however, the molecules must move a longer distance between collisions. Consequently, there are fewer collisions per unit time with the container walls, and pressure decreases. Thus, the model accounts in a simple way for Bovle's law


The above sentence is taken from a textbook. What I don't understand is when molecules collide why would the momentum decrease? I would think the momentum would merely be preserved or transferred from one atom to another, just like with billiard balls which are not affected by gravity.

 

[NobodySpecial]

It doesn't say the momentum decreases.

The number of colisions / time with the container walls decreases which gives a less force on the walls and so a lower measured pressure.

Note in an ideal gas you ignore any collisions between the gas molecules.

 

[bobsmith76]

Never mind, I think I got it. It's collisions with the walls of the container, not collisions with other molecules, that's what I was not understanding. If the container is enlarged then the moleculues will hit the container walls less often.

 

[NobodySpecial]

Never mind, I think I got it. It's collisions with the walls of the container, not collisions with other molecules, that's what I was not understanding. If the container is enlarged then the moleculues will hit the container walls less often.

Exactly .

 

[PJC01]

Firstly, it is important to understand that gas molecules are constantly in motion due to their high kinetic energy. This motion is random and can be in any direction. When these molecules collide with each other or with the walls of the container, their momentum changes. This is because momentum is defined as the product of an object's mass and its velocity. So, when a gas molecule collides with another molecule or with the walls of the container, its velocity changes, and therefore its momentum changes as well.

Now, let's consider the scenario described in the content - an increase in volume at constant temperature. As the volume increases, the molecules have more space to move around and therefore, they have to travel a longer distance between collisions. This means that the time between collisions also increases. As a result, there are fewer collisions per unit time with the walls of the container. This decrease in collisions means that there is less force exerted on the walls, resulting in a decrease in pressure.

To summarize, the decrease in pressure at constant temperature is a result of the decrease in the number of collisions per unit time due to the increase in volume. This is because the molecules have to travel a longer distance between collisions, which decreases the frequency of collisions and therefore, the force exerted on the walls. This is how the model accounts for Boyle's law - as volume increases, pressure decreases at constant temperature.