The mean free path of molecules of a gas (rad | vedclass

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(B) The mean free path $\lambda$ of a gas molecule is given by the formula:$\lambda = \frac{1}{\sqrt{2} n \pi d^2}$where $n$ is the number density of

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$r^2$

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(B) The mean free path $\lambda$ of a gas molecule is given by the formula:$\lambda = \frac{1}{\sqrt{2} n \pi d^2}$where $n$ is the number density of molecules and $d$ is the diameter of the molecule.Since the radius of the molecule is $r$,the diameter is $d = 2r$.Substituting this into the formula:$\lambda = \frac{1}{\sqrt{2} n \pi (2r)^2} = \frac{1}{4\sqrt{2} n \pi r^2}$From this expression,it is clear that $\lambda \propto \frac{1}{r^2}$.Therefore,the mean free path is inversely proportional to $r^2$.

The mean free path of molecules of a gas (radius $r$) is inversely proportional to

Similar Questions

Write the equation for the mean free path of gas molecules.

The mean free path of a molecule of diameter $5\times10^{-10} \ m$ at the temperature $41^{\circ}C$ and pressure $1.38\times10^{5} \ Pa$ is given as . . . . . . $m$. (Given $k_{B}=1.38\times10^{-23} \ J/K$).

For a gas,$C_{p} - C_{V} = R$ in state $P$ and $C_{p} - C_{V} = 1.10 R$ in state $Q$. If $T_{P}$ and $T_{Q}$ are the temperatures in states $P$ and $Q$ respectively,then which of the following is true?

Under what conditions does a real gas obey the relation $PV = RT$?

$Assertion:$ Mean free path of a gas molecule varies inversely as the density of the gas.
$Reason:$ Mean free path varies inversely as the pressure of the gas.

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