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Q.

Express the average kinetic energy per mole of a monoatomic gas of molar mass $M$ , at temperature $T$ , $K$ in terms of the average speed of the molecules $U_{avg}$ :

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a

$\frac{8 M}{3 π} U_{avg}^{2}$

b

$(\frac{3 πM}{16}) U_{avg}^{2}$

c

$\frac{3 M}{16} U_{avg}^{2}$

d

$(\frac{2 M}{π}) U_{avg}^{2}$

answer is D.

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Detailed Solution

Average speed of the molecule;

$U_{avg} = \sqrt{\frac{8 RT}{πm}}$

$\Rightarrow U_{avg}^{2} \times \frac{πM}{8} = RT$

$KE = \frac{3}{2} RT = (\frac{3 πM}{16}) U_{avg}^{2}$

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