Question

If m represents the mass of each molecule of a gas and T, its absolute temperature, then the root mean square velocity of the gaseous molecule is proportional to

• A. $mT$
• B. $m^{1/2}{T}^{1/2}$
• C. $m^{-1/2}T$
• D. $m^{-1/2}{T}^{1/2}$
• E. $m{T}^{-1/2}$

Answer 1

The correct option is D $m^{-1/2}{T}^{1/2}$

We know that,
Thermal equilibrium and kinetic interpretation of temperature
${\overline{V}}^2=\frac{3RT}{M}$
$V_{mrs}=\sqrt{\frac{3RT}{M}}$
So, $V_{mrs}\propto \sqrt{T}$
and $V_{mrs}\propto \frac{1}{\sqrt{m}}$
The root mean square speed of the molecules of a gas is directly proportional to the square root of the absolute temperature of the gas and inversely proportional to the square root of the mass of molecules of the gas.
$V_{rms}=m^{-1/2}\times T^{1/2}$