Question

A cubical box of side of $1m$ contains helium gas (atomic weight $4$) at a pressure of $100N/m^2$. During an observation time of $1s$, an atom traveling with the root-mean-square speed parallel to one of the edges of the cube, was found to make $500$ hits with a particular wall, without any collision with other atoms. Evaluate the temperature (in $K$) of the gas. (Take $R=$ $25/3Jmo{l}^{-1}{K}^{-1}$ and $k=1.38\times 10^{-23}J/K)$

Answer 1

Answer: 160

$v_{rms}=\sqrt{\frac{3RT}{M}}$
Since gas molecule makes $500$ collisions in $1s$,
$\therefore$ Distance travelled in $1s=1000m$
$\therefore$ From the given relation,
$\sqrt{\frac{3RT}{M}}=1000$
$\Rightarrow 3\times \frac{25}{3}\times T\times \frac{1}{4\times 10^{-3}}=10^6$
$\Rightarrow T=160K$