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. m T
• 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

Answer: (D)

We know that,
Thermal equilibrium and kinetic interpretation of temperature
${\bar{v}}^2=\frac{3RT}{M}$
$V_{rms}=\sqrt{\frac{3RT}{M}}$
So $V_{rms}\propto \sqrt{T}$
and $V_{rms}\propto \frac{1}{\sqrt{m}}$
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.
$V_{rms}=m^{-1/2}\times T^{1/2}$