An inverted bell lying at the bottom of a lake $47.6\,m$ deep has $50\, cm^3$ of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be …… $cm^3$ (atmospheric pressure $= 70\, cm$ of $Hg$ and density of $Hg = 13.6\, g/cm^3$)

A mixture of $2\, moles$ of helium gas (atomic mass $= 4\, amu$) and $1\, mole$ of argon gas (atomic mass $= 40\, amu$) is kept at $300\, K$ in a container. The ratio of the $r.m.s.$ speeds $\left( {\frac{{{v_{rms\,}}{\rm{(helium)}}\,}}{{{v_{rms}}\,{\rm{(argon)}}}}} \right)$ is

Two identical containers $A$ and $B$ with frictionless pistons contain the ideal gas at the same temperature and the same volume $V$. The mass of the gas in $A$ is $m_A$ and in $B$ is $m_B$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2V$. The changes in pressure in $A$ and $B$ are found to be $\Delta p$ and $1.5\Delta P$ respectively. Then

A vessel contains $1\, mole$ of $O_2$ gas (molar mass $32$) at a temperature $T$. The pressure of the gas is $P$. An identical vessel containing one mole of $He$ gas (molar mass $4$) at a temperature $2T$ has a pressure of

The translational kinetic energy of gas molecule for one mole of the gas is equal to