Questions in Kinetic Theory of Gases

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One mole of ideal monoatomic gas $(\gamma =5/3)$ is mixed with one mole of diatomic gas $(\gamma =7/5).$ What is $\gamma $ for the mixture? $\gamma $ denotes the ratio of specific heat at constant pressure, to that at constant volume
A gaseous mixture contains equal number of hydrogen and nitrogen molecules. Specific heat measurements on this mixture at temperatures below 100 K would indicate that the value of $\gamma $ (ratio of specific heats) for this mixture is
One mole of monoatomic gas and three moles of diatomic gas are put together in a container. The molar specific heat (in $J\,{{K}^{-1}}\,mo{{l}^{-1}})$ at constant volume is $(R=8.3\,J\,{{K}^{-1}}\,mo{{l}^{-1}})$
The temperature of argon, kept in a vessel, is raised by $1^\circ C$ at a constant volume. The total heat supplied to the gas is a combination of translational and rotational energies. Their respective shares are
On giving equal amount of heat at constant volume to 1 mol of a monoatomic and a diatomic gas the rise in temperature $(\Delta T)$ is more for
The kinetic energy, due to translational motion, of most of the molecules of an ideal gas at absolute temperature T is
The number of translational degrees of freedom for a diatomic gas is
The value of the gas constant (R) calculated from the perfect gas equation is 8.32 joules/gm mole K, whereas its value calculated from the knowledge of ${{C}_{P}}$ and ${{C}_{V}}$ of the gas is 1.98 cal/gm mole K. From this data, the value of $J$ is
For a gas if ratio of specific heats at constant pressure and volume is $\gamma$ then value of degrees of freedom is
The ratio of specific heat of a mixture of one mole of helium and one mole of hydrogen gas will be

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