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?

$A$ real gas behaves as an ideal gas at

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

$Assertion:$ Mean free path of a gas molecule varies inversely as the density of the gas.
$Reason:$ Mean free path varies inversely as the pressure of the gas.

For matter to exist simultaneously in gas and liquid phases:

The mean free path of molecules of a certain gas at $STP$ is $1500\,d$,where $d$ is the diameter of the gas molecules. While maintaining the standard pressure,the mean free path of the molecules at $373\,K$ is approximately $..........\,d$