Question

If $10^{22}$ gas molecules each of mass $10^{-26}$ kg collide with a surface (perpendicular to it) elastically per second over an area $1\, m^2$ with a speed $10^4$ m/s, the pressure exerted by the gas molecules will be of the order of :

• A. $10^8 \; N/m^2$
• B. $10^4 \; N/m^2$
• C. $10^3 \; N/m^2$
• D. $10^{16} \; N/m^2$

Answer 1

Answer: (C)

$10^3 \; N/m^2$

Answer 2

Magnitude of change in momentum per collision = 2 mv
$\text{Pressure} = \frac{\text{Force}}{\text{Area}} = \frac{N\left(2mv\right)}{1}$
$= \frac{10^{22} \times2\times10^{-26}\times10^{4}}{1}$
$=2N/m^{2}$