At S.T.P., the mean free path of gas molecule is 1500 d , where 'd' is diameter of molecule. What will be…

At S.T.P., the mean free path of gas molecule is 1500 d , where 'd' is diameter of molecule. What will be the mean free path at 373 K at constant volume?
  1. 1500 d
  2. $\frac{373}{273} \times 1500 \mathrm{~d}$
  3. $\frac{273}{373} \times 1500 \mathrm{~d}$
  4. $\sqrt{\frac{373}{273}} \times 1500 \mathrm{~d}$

Solution

We know, $\begin{array}{ll} & \text { Mean free path } \lambda=\frac{\mathrm{k}_{\mathrm{B}} \mathrm{~T}}{\sqrt{2} \pi \mathrm{~d}^2 \mathrm{P}} \Rightarrow \lambda \propto \mathrm{~T} \\ \therefore \quad & \frac{1500 \mathrm{~d}}{\lambda}=\frac{273}{373} \\ & \lambda=1500 \mathrm{~d} \times \frac{373}{273} \end{array}$

Asked in: MHT CET 2024 (02 May Shift 1)

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