Considering the gases to be ideal, the value of $\gamma = \frac{{{C_P}}}{{{C_V}}}$ for a gaseous mixture consisting of $= 3$ moles of carbon dioxide and $2$ moles of oxygen will be $({\gamma _{{O_2}}} = 1.4,\,\,{\gamma _{C{O_2}}} = 1.3)$
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Consider a $1\, c.c.$ sample of air at absolute temperature ${T_0}$ at sea level and another $1 cc$ sample of air at a height where the pressure is one-third atmosphere. The absolute temperature $T$ of the sample at that height is
A cubical box with porous walls containing an equal number of ${O_2}$ and $H_2$ molecules is placed in a large evacuated chamber. The entire system is maintained at constant temperature $T.$ The ratio of ${v_{rms}}$ of ${O_2}$ molecules to that of the ${v_{rms}}$ of $H_2$ molecules, found in the chamber outside the box after a short interval is
A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at $300 K$. The ratio of the average rotational kinetic energy per ${O_2}$ molecule to that per ${N_2}$ molecule is
When an air bubble of radius $‘r’$ rises from the bottom to the surface of a lake, its radius becomes $5r/4$ (the pressure of the atmosphere is equal to the $10 \,m$ height of water column). If the temperature is constant and the surface tension is neglected, the depth of the lake is .... $m$
In the two vessels of same volume, atomic hydrogen and helium at pressure $1\, atm$ and $2\, atm$ are filled. If temperature of both the samples is same, then average speed of hydrogen atoms $ < {C_H} > $ will be related to that of helium $ < {C_{He}} > $ as