What is the relationship between temperature and pressure in gas laws?

[Ryder S]

Hi all...!

Gas laws.

Sorry about the simplicity of the question, but that should make it easy :)

I have two rigid containers open to air. One is 10 times the volume of the other.

I cap each.

I increase the temperature of each, 50 degrees.

What can I say about the pressure inside the containers, compared to each other?

A brief explanation?

Thanks ever so much.

 

[gralla55]

The pressure will be the same.

Just look at the ideal gas law:

PV = nRT, here P is pressure, V is volume, n is the number of molecules and T is the temperature. R is just a constant.

Solving for P you get:

P = nRT / V

Now, right after you close the lid on each container, notice that the number of molecules in each container is directly proportional to the volume of the container. Therefore the pressure will be the same. When you increase the temperature, it is proportional to the pressure in both cases, so when you increase the temperature equally much in both containers, you increase the pressure equally much. So the end pressure is the same.

 

[Ryder S]

Thanks... this is how I see it as well... but I'm in disagreement with a PhD about it... (I'm not one, so I have less cred), so I appreciate the sanity check.

I just think of a (very tough) soap bubble in a pressure cooker.

If you add or subtract heat... he would have to believe that the bubble would change size one way or the other as you changed temperature.

Intuitively, I just couldn't see that happening. The gas would become equally more active on both sides of the bubble, so the bubble would retain its size. The only way to change the bubble size would be to add or remove gas... so even if the bubble was slowly permeable... there would be no net exchange (discounting surface tension of the bubble, of course :)

 

[nasu]

It's not quite the same problem.
The gas inside the bubble has a higher pressure than the environment, to start with.
In your OP both containers have the same initial pressure.

 

[cjl]

It's not quite the same problem.
The gas inside the bubble has a higher pressure than the environment, to start with.
In your OP both containers have the same initial pressure.

I would tend to think a bubble would be pretty close to zero gauge pressure - in other words, the same pressure as the environment.

 

[Ryder S]

That's why I said:

"discounting surface tension of the bubble, of course :)"

So there you go.

Thanks to all!