Question

The root mean square speed of a gas of density $1.5$ g/ litre at a pressure of $2\times {10}^{6}N/m^2$ is .

• A. $2\times {10}^{6}m/s$
• B. $2\times {10}^{8}cm/s$
• C. $2\times {10}^{3}m/s$
• D. $2\times {10}^{2}cm/s$

Answer 1

The correct option is C $2\times {10}^{3}m/s$

The density of a gas is $1.5g/litre$ or $1.5kg/m^3$ and the pressure is $2\times {10}^{6}N/m^2$.

The root mean square speed is given as,

$\overline{c}=\sqrt{\frac{3P}{\rho }}$

$=\sqrt{\frac{3\times 2\times {10}^6}{1.5}}$

$=2\times {10}^{3}m/s$

Thus, the root mean square speed of gas is $2\times {10}^{3}m/s$