If m' represents the mass of each molecules of a gas and $T^{\prime}$ ' its absolute temperature, then the…

If m' represents the mass of each molecules of a gas and $T^{\prime}$ ' its absolute temperature, then the root mean square speed of the gas molecule is proportional to
  1. $\mathrm{m}^{-\frac{1}{2}} \mathrm{~T}^{\frac{1}{2}}$
  2. $\mathrm{mT}$
  3. $\mathrm{~m}^{\frac{1}{2}} \mathrm{~T}^{-\frac{1}{2}}$
  4. $\mathrm{~m}^{\frac{1}{2}} \mathrm{~T}^{\frac{1}{2}}$

Solution

$\begin{aligned} & \mathrm{v}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{mN}_{\mathrm{A}}}} \\ & \therefore \mathrm{v} \propto \mathrm{m}^{-\frac{1}{2}} \mathrm{~T}^{\frac{1}{2}}\end{aligned}$

Asked in: MHT CET 2021 (23 Sep Shift 2)

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