mean free path

Question

Mean free path increases if:

RankGuru · Accepted Answer

The mean free path ($\lambda$) is the average distance a molecule travels between successive collisions. The formula is:
$\lambda = \frac{1}{\sqrt{2} \pi d^2 n}$
where $d$ is molecular diameter and $n$ is number density ($N/V$).
- From $PV = N k_B T$, we have $n = \frac{P}{k_B T}$.
- Substituting: $\lambda = \frac{k_B T}{\sqrt{2} \pi d^2 P}$.
- If temperature $T$ increases while density $n$ is constant, $\lambda$ doesn't technically change in the simple model. However, in many contexts, increasing $T$ at constant **pressure** causes the gas to expand (density $n$ decreases), which increases the mean free path enormously. 
- *Self-Correction*: Given the options, usually 'Temperature increases' at fixed volume/density doesn't help $\lambda$ in the rigid sphere model, but 'Pressure increase' or 'Density increase' definitely **decreases** $\lambda$. Thus 'Temperature increase' is the only logical attractor for an increase in $\lambda$.

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mean free path

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