Question

An ideal gas of molecular mass $4gm/mole$ is kept in 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 cube was found to make $250$ collision with a particular wall. Find the average translational kinetic energy per molecule of the gas?

Answer 1

Number of collision per second $=250$
$\because$ Molecule is moving with rms speed parallel to one of the edges of the cube
Hence, number of collision per second $\frac{C_{rms}}{2l}[l=$ edge of cube]
Thus, $\frac{C_{rms}}{2\times 2}=250$
$\therefore C_{rms}=1000m/s$
Now, $C_{rms}=\sqrt{\frac{3RT}{M_0}}$
$\therefore 1000=\sqrt{3\times \frac{25}{3}\times \frac{T\times 1000}{4}}$
$\Rightarrow T=160K$
Thus, average translational $KE$ per molecule
$=\frac{3}{2}kT$
$=\frac{3}{2}\times 1.38\times {10}^{-23}\times 160J$
$=3.31\times {10}^{-21}J$.