Question

The r.m.s velocity of $CO$ gas molecules at ${27}^{o}C$ is approximately 1000 m/s. For $N_2$ molecules at 600 K, the r.m.s velocity is approximately:

• A. 2000 m/s
• B. 1414 m/s
• C. 1000 m/s
• D. 1500 m/s

Answer 1

The correct option is B 1414 m/s

$u_{rms}=\sqrt{\frac{3RT}{M}}$

$\frac{u_{rms,N_2}}{u_{rms,CO}}=\sqrt{\frac{T_{N2}{M}_{CO}}{T_{CO}{M}_{N2}}}$

$\frac{u_{rms,N_2}}{1000}=\sqrt{\frac{600\times 28}{300\times 28}}$

$u_{rms,N2}=1414m/s$

Option B is the answer.