Let $\gamma_1$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and $\gamma_2$ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio, $\frac{\gamma_1}{\gamma_2}$ is
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A vessel of volume $0.02 \,\,m^3$ contains a mixture of hydrogen and helium at $20\,^oC$ and $2$ atmospheric pressure. The mass of mixture is $5\,\, gms$. Find the ratio of mass of hydrogen to that of helium in the mixture.
$Assertion :$ Mean free path of a gas molecules varies inversely as density of the gas.
$Reason :$ Mean free path varies inversely as pressure of the gas.
An ideal gas is trapped inside a test tube of cross-sectional area $20 \times 10^{-6} \,\,m^2$ as shown in the figure. The gas occupies a height $L_1$ at the bottom of the tube and is separated from air at atmospheric pressure by a mercury column of mass $0.002\,\, kg$. If the tube is quickly turned isothermally, upside down so that $L_2$ mercury column encloses the gas from below. The gas now occupies height $L_1$ in the tube. The ratio $L_1$ is [Take atmospheric pressure $= 10^5 Nm^{-2}]$