At $S.T.P.$,the mean free path of a gas molecule is $1500 \ d$,where '$d$' is the diameter of the molecule. What will be the mean free path at $373 \ K$ at constant volume?

If the volume of the gas containing $n$ number of molecules is $V,$ then the pressure will decrease due to the force of intermolecular attraction in the proportion:

$A$ fixed amount of nitrogen gas ($1$ mole) is taken and subjected to pressure and temperature variations. The experiment is performed at high pressures and various temperatures. The results obtained are shown in the figure. The correct variation of $PV/RT$ with $P$ for nitrogen gas at high temperatures will be exhibited by:

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 $k = 1.38 \times 10^{-23} \,JK^{-1}$):

The mean free path of gas molecules depends on $(d =$ molecular diameter$)$

An ideal gas is enclosed in a cylinder at a pressure of $2 \, atm$ and a temperature of $300 \, K$. The mean time between two successive collisions is $6 \times 10^{-8} \, s$. If the pressure is doubled and the temperature is increased to $500 \, K$,the mean time between two successive collisions will be close to: