Question

An ideal gas of molecular mass $4gm/mole$ is kept in a cubical container of edge $2m$. During an observation time of $1$ second, the molecule, moving with rms speed parallel to one of the edges of the cube was found to make $250$ collision with a particular wall. Find the average translational kinetic energy per molecule of the gas?

Answer 1

$250=\frac{U_{rms}}{2}$ [Collision frequency$=\frac{U_{rms}}{\lambda }$]

Now, $PV=\frac{1}{3}mn{U}_{rms}^2$

where $n=$ no. of moles

$m=$ mass/mole

$\Rightarrow nRT=\frac{1}{3}mn{U}_{rms}^2\Rightarrow nRT=\frac{1}{3}m{U}_{rms}^2$

KE/molecules$=\frac{3}{2}KT=\frac{3}{2}\frac{RT}{N}$

$=\frac{3}{2}\frac{1}{3}\frac{m{U}_{rms}^2}{N}=\frac{1}{2}\times \frac{4\times {10}^{-3}\times 500}{1.38\times {10}^{-23}}=\frac{1}{2}\times \frac{2}{1.38\times {10}^{-22}}J/molecule=7.2429\times {10}^{22}J/molecule$