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The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth is closest to : [Boltzmans Constant $k_B = 1.38\times10^{-23}\, J / K$ Avogadro number $N_A = 6.02\times10^{26}\, / kg$ Radius of Earth $: 6.4\times10^6\, m$ Gravitation acceleration on Earth $= 10\, ms^{-2}$]
A vessel of volume 20L contains a mixture of hydrogen and helium at temperature of $27^{\circ} C$ and pressure $2 atm$. The mass of mixture is $5 g$. Assuming the gases to be ideal, the ratio of mass of hydrogen to that of helium in the given mixture will be
$1\ mole$ of a gas with $\gamma$ = $7/5$ is mixed with $1\ mole$ of a gas with $\gamma$ = $5/3$, then the value of $\gamma$ for the resulting mixture 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 flask contains hydrogen and oxygen in the ratio of $2: 1$ by mass at temperature $27^{\circ} C$. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is :
The pressure $P,$ volume $V$ and temperature $T$ of a gas in the jar $A$ and the other gas in the jar $B$ at pressure $2P,$ volume $V/4$ and temperature $2T,$ then the ratio of the number of molecules in the jar $A$ and $B$ will be