Question

A cubical container having each side as l is filled with a gas having $N$ molecules in the container. Mass of each molecule is $m$. If we assume that at every instant half of the molecules are moving towards the positive $x-axis$ and half of the molecules are moving towards the negative $x-axis$. Two walls of the container are perpendicular to the x-axis. Find the net force acting on the two walls given? Assume that all the molecules are moving with speed $v_0$.

Answer 1

Total pressure inside the container

$PV=nRT$

$P\left(l^3\right)=\left(\frac{N}{N_A}\right)\left(R\right)T$

$P=\left(\frac{N}{N_A}\right)\frac{RT}{\left(l^3\right)}$

force on wall $A\Rightarrow F=PA$

$F=\left(\frac{N}{N_A}\right)\frac{RT}{l^3}\times l^2$

$F=\left(\frac{RT}{l}\right)\left(\frac{N}{N_A}\right)$

same force is on wall $B$

OR $K.E=\frac{1}{2}m{\mu }_0^2=\frac{3}{2}\left(\frac{PV}{N_A}\right)\left(\frac{n}{N_A}\right)$

Calculate pressure in the terms of $V$ and $k=PA$