The $P-T$ graph shows a gas being heated. During this process from point $1$ to $2$,the volume of the gas:

$A$ volume $V$ and pressure $P$ diagram was obtained from state $1$ to state $2$ when a given mass of a gas is subjected to temperature changes. During this process the gas is

The equation of state for $5\,g$ of oxygen at a pressure $P$ and temperature $T$,when occupying a volume $V$,will be where $R$ is the gas constant.

Nitrogen gas $N_2$ of mass $28 \,g$ is kept in a vessel at a pressure of $10 \,atm$ and temperature $57^{\circ} C$. Due to leakage of $N_2$ gas,its pressure falls to $5 \,atm$ and temperature to $27^{\circ} C$. The amount of $N_2$ gas leaked out is .......... $g$.

Two vessels separately contain two ideal gases $A$ and $B$ at the same temperature. The pressure of $A$ is twice that of $B$. Under these conditions,the density of $A$ is found to be $1.5$ times the density of $B$. The ratio of the molecular weights of $A$ and $B$ is:

An air bubble of volume $1.0 \; cm^{3}$ rises from the bottom of a lake $40 \; m$ deep at a temperature of $12 \; ^{\circ}C$. To what volume (in $cm^{3}$) does it grow when it reaches the surface,which is at a temperature of $35 \; ^{\circ}C$?