JEE Main 2019 — Physics solution

JEE Main2019Physics

An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCI molecules in its gaseous phase is $\overset{v}{ˉ}$ , m is its mass and k_B is Boltzmann constant, then its temperature will be :

A
$\frac{m v ˉ ^{2}}{5 k _{B}}$
B
$\frac{m v ˉ ^{2}}{6 k _{B}}$
C
$\frac{m v ˉ ^{2}}{7 k _{B}}$
D
$\frac{m v ˉ ^{2}}{3 k _{B}}$

Solution

$\overset{v}{ˉ} = \frac{3 R T}{M} \overset{v}{ˉ} = \frac{3 R T}{m N _{A}} \overset{v}{ˉ} = \frac{3 k _{B} T}{m}$

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