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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
A certain amount of an ideal monatomic gas needs $20 \,J$ of heat energy to raise its temperature by $10^{\circ} C$ at constant pressure. The heat needed for the same temperature rise at constant volume will be ........ $J$
A container is divided into two equal parts $I$ and $II$ by a partition with a small hole of diameter $d$. The two partitions are filled with same ideal gas, but held at temperatures $T_{ I }=150 \,K$ and $T_{ II }=300 \,K$ by connecting to heat reservoirs. Let $\lambda_{1}$ and $\lambda_{1 I}$ be the mean free paths of the gas particles in the two parts, such that $d >> \lambda_{ I }$ and $d >> \lambda_{ II }$. Then, the $\lambda_{ I } / \lambda_{ II }$ is close to
At constant pressure, the ratio of increase in volume of an ideal gas per degree raise in kelvin temperature to it's original volume is $(T =$ absolute temperature of the gas$)$