States of Matter - Result Question 17
####17. For a monatomic gas kinetic energy $=E$. The relation with rms velocity is
(a) $u=\left(\frac{2 E}{m}\right)^{1 / 2}$
(b) $u=\left(\frac{3 E}{2 m}\right)^{1 / 2}$
(c) $u=\left(\frac{E}{2 m}\right)^{1 / 2}$
(d) $u=\left(\frac{E}{3 m}\right)^{1 / 2}$
(2004, 1M)
States of Matter 65
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Solution:
- Kinetic energy $(E)=\frac{3}{2} k T$
$$ \begin{aligned} \text { RMS speed }(u) & =\sqrt{\frac{3 k T}{m}} \ \Rightarrow \quad u & =\sqrt{\frac{2 E}{m}} \end{aligned} $$
