Does Increasing Molecules in a Constant Temperature Container Affect Pressure?

[Wombat11]

Homework Statement

If number of molecules in a closed container increases and it is kept at a constant tempurature, what happens to the pressure?

I was confused because I thought if you add molecules the temputature would go up so keeping temputature a constant would have no affect on the pressure.[/B]

 

[Fightfish]

I was confused because I thought if you add molecules the temputature would go up

Why would you think that? What aspect of the system does temperature characterise?

Also, as per the title of your post, a good starting point for this question would be to start by writing down the ideal gas equation. That being said, it is still important to understand the physical meaning of the various quantities present in the ideal gas law.

 

[Valour549]

Temperature is a measure of the average kinetic energy of the molecules. This means whether the container has 10 molecules or 100 molecules, it's very much possible that the temperature be kept the same.

Let's pretend the average kinetic energy (per molecule) inside the 10-molecule container is 1J. And likewise for the 100-molecule container, since they have the same temperature. The first container is going to have 10 molecules each with 1J, bouncing around, hitting each other and also the walls of the container (which causes force and pressure). The second container has, in comparison, 100 molecules each with 1J bouncing around.

Impact with walls of the second container happens more frequently, as a result there is a greater average force, and thus greater pressure.

Alternatively, you can look at the ideal gas law, PV = nRT.
V is the same, since the volume of the container doesn't change. T is the same, since we're keeping temperature constant. R is a constant. As you add molecules n (the amount of molecules in moles) increases. Therefore the pressure P increases accordingly.