If $n$ is the number density and $d$ is the diameter of the molecule,then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

If the mean free path of atoms is doubled,then the pressure of the gas will become:

$A$ container is divided into two equal parts $I$ and $II$ by a partition with a small hole of diameter $d$. The two parts are filled with the same ideal gas,but held at temperatures $T_{I} = 150 \, K$ and $T_{II} = 300 \, K$ by connecting them to heat reservoirs. Let $\lambda_{I}$ and $\lambda_{II}$ be the mean free paths of the gas particles in the two parts,such that $d \gg \lambda_{I}$ and $d \gg \lambda_{II}$. Then,the ratio $\lambda_{I} / \lambda_{II}$ is close to:

For a gas,$C_{p} - C_{V} = R$ in state $P$ and $C_{p} - C_{V} = 1.10 R$ in state $Q$. If $T_{P}$ and $T_{Q}$ are the temperatures in states $P$ and $Q$ respectively,then which of the following is true?

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion,the average time of collision between molecules increases as $V^q$,where $V$ is the volume of the gas. The value of $q$ is $\left( \gamma = \frac{C_P}{C_V} \right)$.

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