The Ideal Gas Law and Temperature Changes

[nbasma20]

A cylinder containing gas at 300 K is divided into two parts, A and B, of equal volume by a frictionless piston of cross-sectional area of 15 cm 2. Each part has a volume of 100 cm 3 and equal initial pressure. The temperature of the gas in part A is raised to 373 K, while the part B is maintained at the original temperature. The piston and walls are perfect insulators. Calculate
how far will the piston move due to the change in temperature.

 

[gneill]

Hi nbasma20. Welcome to Physics Forums.

In order to get help here you should follow the suggested post outline, including what you feel are equations relevant to your problem, and your own attempt at a solution (or at least the things you've tried so far).

So what are your thoughts on how to approach the problem? What laws do you think might be applicable?

 

[nbasma20]

Not sure at all.

I suppose the distance moved by the piston can be worked out from

W = - p A dx

But how to calculate W?

I have no idea where to begin.

 

[gneill]

Have you looked at the ideal gas law and how it might be of use?

The piston is apparently massless, and it's free to move if there's a force differential. What does that tell you about the pressure in both chambers?

 

[nbasma20]

We know that the initial pressure is equal in each part.

And how can I make use of pV = nRT?

Thanks

 

[gneill]

We know that the initial pressure is equal in each part.

And how can I make use of pV = nRT?

Thanks

Just the initial pressure? Think about it. How would a pressure difference be maintained if the piston is free to move?

PV = nRT applies to gasses! You've got gas in both chambers, and more than that, you know that here is an equal amount of gas in each chamber (n is the same). Further, they are starting with the same volume, pressure, and temperature. What about the total volume of the gas (sum of the volumes of each chamber)?

If the gas in chamber B is being maintained at the initial temperature, what does that say about the product P*V for that chamber?