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:

  1. Kinetic energy $(E)=\frac{3}{2} k T$

$$ \begin{aligned} \text { RMS speed }(u) & =\sqrt{\frac{3 k T}{m}} \ \Rightarrow \quad u & =\sqrt{\frac{2 E}{m}} \end{aligned} $$



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