An ideal gas of molar mass ' $\mathrm{M}_0$ ' has r.m.s. velocity ' $\mathrm{V}$ ' at temperature '…

An ideal gas of molar mass ' $\mathrm{M}_0$ ' has r.m.s. velocity ' $\mathrm{V}$ ' at temperature ' $\mathrm{T}$ '. Then
  1. $\mathrm{VT}^2=$ constant
  2. $\frac{\mathrm{V}^2}{\mathrm{~T}}=$ constant
  3. $\mathrm{V}^2 \mathrm{~T}=$ constant
  4. $\mathrm{V}$ is independent of $\mathrm{T}$

Solution

R.M.S. velocity is given by $\begin{aligned} & \mathrm{V}=\sqrt{\frac{3 R T}{\mathrm{M}_0}} \\ & \therefore \mathrm{V}^2=\frac{3 \mathrm{RT}}{\mathrm{M}_0} \\ & \therefore \frac{\mathrm{V}^2}{\mathrm{~T}}=\frac{3 \mathrm{R}}{\mathrm{M}_0}=\text { constant } \end{aligned}$ :

Asked in: MHT CET 2021 (22 Sep Shift 2)

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