Question

1.2 moles of a gas is present in a piston fitted cylinder with volume V at temperature 200 K. Gas has mean free path of 2.25 m. If piston is moved out to have 2V volume and temperature is raised to 400 K then what will be new mean free path (in m) of the gas

Answer 1

Mean free path $\left(\lambda \right)=\frac{1}{\sqrt{2}\pi d^2\frac{n}{V}}$ where $n$ is number of gas molecules.
Mean free path $\left(\lambda \right)$ does not depend on the temperature at given volume. This is another form of the same equation which has a dependency on pressure, temperature and the Boltzmann constant.
Since the volume increases to 2V, the new mean free path will be $2\times 2.25=4.5m$.