Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A gas is in a cylinder with a piston. Its pressure is halved while its temperature rises from to . By what factor does the mean free path change? In a second test, the same gas is heated from to in a sealed rigid box. By what factor does the mean free path change now?
A molecule of diameter hits every molecule whose centre lies within of its path. With :
Collision frequency .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The cylinder. is proportional to . The temperature grows by and the pressure falls by a factor of 2. So grows by .
Step 2. The sealed box. depends only on and . Neither changes. The factor is .
Watch out. In the box the pressure also rises by 1.5. The rise in and the rise in cancel.
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