Question

The mass of hydrogen molecule is $3.32\times {10}^{-27}\text{kg}$. If ${10}^{23}$ hydrogen molecules strike per second at $2{\text{cm}}^2$ area of rigid wall of a close container normally and rebound back with the speed of $1000\text{m/s}$, then the pressure exerted on the wall (according to kinetic theory of gas) is

• A. $3000{\text{N/m}}^2$
• B. $6640{\text{N/m}}^2$
• C. $8320{\text{N/m}}^2$
• D. $3320{\text{N/m}}^2$

Answer 1

The correct option is D $3320{\text{N/m}}^2$

According to kinetic theory, collision between molecules and wall of container is perfectly elastic.
$\therefore$Change in momentum,
$\left|\left(\Delta P\right)\right|=|P_f-P_i|=2mv$
where $v$ is rebound velocity of molecule
We know that
$F=\frac{\Delta P}{\Delta t}$
$\therefore$ Force exerted by 1 molecule in $1\text{sec}$
$F_1=2mv\text{N}$
$\therefore$ Force exerted by ${10}^{23}$ molecule in $1\text{sec}$
$=2mv\times {10}^{23}\text{N}$
Pressure exerted by ${10}^{23}$ molecule
$=\frac{2\times mv\times {10}^{23}}{\text{Area}}$
$=\frac{2\times m\times v\times {10}^{23}}{2\times {10}^{-4}{\text{m}}^2}$
$=\frac{2\times 3.32\times {10}^{-27}\times {10}^3\times {10}^{23}}{2\times {10}^{-4}}$
$=3320{\text{N/m}}^2$