Question

The density of an ideal gas is $6\times {10}^{-2}{\text{kg/m}}^3$ and the root mean square velocity of the gas molecules is $500\text{m/s}$. The pressure exerted by the gas on the walls of the vessel is

• A. $5\times {10}^3{\text{N/m}}^2$
• B. $1.2\times {10}^{-4}{\text{N/m}}^2$
• C. $0.75\times {10}^{-4}{\text{N/m}}^2$
• D. $40{\text{N/m}}^2$

Answer 1

The correct option is A $5\times {10}^3{\text{N/m}}^2$

We know that
Pressure $P=\frac{1}{3}\rho v_{\text{rms}}^2$
Where $\rho =$ density of gas
$\Rightarrow P=\frac{1}{3}\times 6\times {10}^{-2}\times {500}^2$
$=5000{\text{N/m}}^2$
$=5\times {10}^3{\text{N/m}}^2$