Solving Gas Expansion in Equal Containers

[emily710]

Homework Statement

The problem states: Two small containers of equal volume, 100 cm^3, each contain helium gas at 0 degrees C and 1.00 atm pressure. The two containers are joined by a small open tube of negligible volume, allowing gas to flow from one container to the other. What common pressure will exist in the two containers if the temperature of one container is raised to 100 degrees C while the other is kept at 0 degrees C.

Homework Equations

I know I should use PV=nRT but I am having trouble with how to set the pressures equal.

The Attempt at a Solution

I used n=PV/RT to find the number of moles of Helium gas in each container = 4.4646*10^-6 mol He

I then tried to use: n1T1=n2T2 to find the number of moles of He on the side of the container that was heated to 100 degrees C, but am stuck here.

*Would the pressure rise the same amount if both sides of the container were heated to 50 degrees C?

 

[Mapes]

Hi emily710, welcome to PF. Why are you stuck there? You know the individual temperatures, so you can figure out the ratio between the amounts of helium in the two containers. And you also know the total amount of helium, so you should be able to calculate the individual amounts along with the common pressure.

You can use these equations to answer your last question.

 

[LowlyPion]

Welcome to PF.

You need to use a little bit of manipulation to arrive at the answer.

PV =nRT you know.

So express the things that are constant, in the things that vary.

P/T = nR/V for each container right?

When they are connected then you have

Po1/To1 + Po2/To2 = 2*nR/V

When you heat 1 vessel, looks like you get:

P'1/(To1+100) + P'2/To2 = 2*nR/V

Now substitute for the things that are still constant.