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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


Solution

Mean free path (λ)=12πd2nV where n is number of gas molecules.
Mean free path (λ) 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 2×2.25=4.5 m

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