An insulated cylinder of volume $60\,cm^{3}$ is filled with a gas at $27^{\circ}C$ and $2$ atmospheric pressure. Then the gas is compressed making the final volume $20\,cm^{3}$ while allowing the temperature to rise to $77^{\circ}C$. The final pressure is . . . . . . atmospheric pressure.

$A$ $20 \,cm$ long tube is closed at one end. It is held vertically,and its open end is dipped in water until only half of it is outside the water surface. Consequently,water rises in it by height $h$ as shown in the figure. The value of $h$ is closest to (assume that the temperature remains constant,$P_{\text{atm}} = 10^5 \,N/m^2$,density of water $\rho = 10^3 \,kg/m^3$,and acceleration due to gravity $g = 10 \,m/s^2$): (in $,cm$)

The volume of a gas at pressure $21 \times 10^4 \ N/m^2$ and temperature $27^\circ C$ is $83 \ L$. If $R = 8.3 \ J/mol/K$,then the quantity of gas in $gm-mole$ will be:

The correct graph between pressure $(P)$ and density $(\rho)$ of a gas at constant temperature is

The perfect gas equation for $4 \ g$ of hydrogen gas is

State Boyle's law and Charles's law.