Question

According to kinetic theory of gases:

• A. The pressure exerted by a gas is proportional to mean square velocity of the molecules
• B. The pressure exerted by the gas is proportional to the root mean square velocity of the molecules
• C. The Root mean square velocity is inversely proportional to the temperature
• D. The mean translational $KE$ of the molecule is directly proportional to the absolute temperature

Answer 1

The correct option is D The mean translational $KE$ of the molecule is directly proportional to the absolute temperature

Postulates of Kinetic theory of gases

The pressure of the gas is due to the continuous collision of molecules on the walls of container. Pressure P = Force/Area.

Maxwell also derived an equation on the basis of above assumption as

$pV=\frac{1}{3}mn{u}^2$

Where $p$ = pressure of gas, $V$ = volume of gas, $m$ = mass of one molecule of gas, $n$ = no. of molecules of gas, $u$ = root mean square velocity of molecules

For 1 mole $n$ = $N$ is Avogadro number

$m\times N=$ Molecular mass $M$

$PV=\frac{1}{3}M{u}^2$

$\Rightarrow u^2=\frac{3pV}{M}$

For 1 mole of an Ideal gas, $PV=RT$

so, $u^2=\frac{3RT}{M}$

$\Rightarrow u=\sqrt{\frac{3PV}{M}}=\sqrt{\frac{3RT}{M}}$