Question

The mean free path $\left(\lambda \right)$ for an ideal gas at constant pressure with molecular diameter $d$ in terms of absolute temperature $T$ has relation -

• A. $\lambda \propto T$
• B. $\lambda \propto \sqrt{T}$
• C. $\lambda \propto \frac{1}{T}$
• D. $\lambda \propto T^2$

Answer 1

The correct option is A $\lambda \propto T$

Mean free path is given by,
$\lambda =\frac{1}{\sqrt{2}\pi n{d}^2}$

$PV=N{k}_{B}T$

$n=\frac{N}{V}=\frac{P}{k_{B}T}$

$\Rightarrow \lambda =\frac{k_{B}T}{\sqrt{2}\pi d^{2}P}$

As pressure$\left(P\right)$ and molecular diameter $\left(d\right)$ are constant, hence $\lambda \propto T$.