Heat and Thermodynamics 4 Question 19
21. A mixture of 2 moles of helium gas (atomic mass $=4 amu$ ) and 1 mole of argon gas (atomic mass $=40 amu$ ) is kept at $300 K$ in a container. The ratio of the rms speeds $\left(\frac{v _{\text {rms }}(\text { helium })}{\left.v _{\text {rms }} \text { (argon }\right)}\right)$ is
(2012)
(a) 0.32
(b) 0.45
(c) 2.24
(d) 3.16
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Solution:
- $\quad v _{rms}=\sqrt{\frac{3 R T}{M}} \quad$ or $\quad v _{rms} \propto \frac{1}{\sqrt{M}}$
$\therefore \quad \frac{\left(v _{rms}\right) _{He}}{\left(v _{rms}\right) _{Ar}}=\sqrt{\frac{M _{Ar}}{M _{He}}}=\sqrt{\frac{40}{4}}=\sqrt{10} \approx 3.16$
