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. $m^{ - 1/2} T^{1/2}$

Answer 1

Answer: (D)

$m^{ - 1/2} T^{1/2}$

Answer 2

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