$A$ balloon contains $500 \ m^3$ of helium at $27^{\circ}C$ and $1 \ atm$ pressure. The volume of the helium at $-3^{\circ}C$ temperature and $0.5 \ atm$ pressure will be ..... $m^3$.

Absolute zero $(0\, K)$ is that temperature at which

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 $Hg = 13.6 \ g/cm^3$)

Two vessels separately contain two ideal gases $A$ and $B$ at the same temperature. The pressure of gas $A$ is three times the pressure of gas $B$. Under these conditions,the density of gas $A$ is found to be two times the density of $B$. The ratio of molecular weights of gas $A$ and $B$ i.e. $\frac{M_A}{M_B}$ is

The volume of a given mass of a gas at $27^{\circ} C$ and $1$ $atm$ is $100$ $cc$. What will be its volume at $327^{\circ} C$ if the pressure remains constant (in $cc$)?

An open and wide glass tube is immersed vertically in mercury in such a way that a length of $0.05 \, m$ extends above the mercury level. The open end of the tube is closed and the tube is raised further by $0.43 \, m$. The length of the air column above the mercury level in the tube will be ...... $m$. Take $P_{atm} = 76 \, cm$ of mercury.