Question

The root mean square velocity of gas molecules at $0^o$C will be if at N.T.P. its density is $1.43$Kg$/m^3$.

• A. $461$m/s
• B. $164$m/s
• C. $461$cm/s
• D. $164$cm/s

Answer 1

The correct option is A $461$m/s

According to formula

$\Rightarrow P=\frac{1}{3}\rho {\overline{C}}^2$ Where $P$ is pressure of gas

$\overline{C}$ is $rms$ velocity

$\rho$ is density of gas

Given,

$\Rightarrow P=1atm=1.013\times {10}^5$ pascal

$\Rightarrow \rho =1.43kg/m^3$

So, $\overline{C}=\sqrt{\frac{3P}{\rho }}=\sqrt{\frac{3\times 1.013\times {10}^5}{1.43}}$

$\Rightarrow \overline{C}\cong 461$m/s.

Hence, the answer is $461$m/s.