Calculate the value of mean free path $(\lambda)$ for oxygen molecules at temperature $27^{\circ} C$ and pressure $1.01 \times 10^{5} Pa$. Assume the molecular diameter $d = 0.3 nm$ and the gas is ideal. Given Boltzmann constant $k = 1.38 \times 10^{-23} J K^{-1}$. (Result in $nm$)

The mean free path $\ell$ for a gas molecule depends upon the diameter $d$ of the molecule as:

Every real gas behaves as an ideal gas:

Two ideal gas thermometers $A$ and $B$ use oxygen and hydrogen respectively. The following observations are made:

Temperature	Pressure thermometer $A$	Pressure thermometer $B$
Triple-point of water	$1.250 \times 10^{5} \; Pa$	$0.200 \times 10^{5} \; Pa$
Normal melting point of sulphur	$1.797 \times 10^{5} \; Pa$	$0.287 \times 10^{5} \; Pa$

$(a)$ What is the absolute temperature of the normal melting point of sulphur as read by thermometers $A$ and $B$?
$(b)$ What do you think is the reason behind the slight difference in answers of thermometers $A$ and $B$? (The thermometers are not faulty). What further procedure is needed in the experiment to reduce the discrepancy between the two readings?

At a temperature of $314 \,K$ and a pressure of $100 \,kPa$, the speed of sound in a gas is $1380 \,ms^{-1}$. The radius of each gas molecule is $0.5 \,Å$. The frequency of sound at which the wavelength of the sound wave in the gas becomes equal to the mean free path of the gas molecules is (Boltzmann constant $k = 1.38 \times 10^{-23} \,JK^{-1}$):

Gases begin to conduct electricity at low pressure because