How much should the pressure be increased in order to reduce the volume of a given mass of gas by $5 \%$ at a constant temperature (in $\%$)?

$A$ graph between volume $V$ and absolute temperature $T$ is obtained when a given mass of a gas is heated. During the heating process from state-$1$ to state-$2$,the pressure

The floor area of a room is $20 \, m^2$ and its walls are $3 \, m$ high. If the pressure of air in the room is $1 \, atm$ and the temperature is $27 \, ^\circ C$,find the mass of the air in the room. (Take the molar mass of air as $29 \, g/mol$). Given: $1 \, atm = 1.01 \times 10^5 \, N \, m^{-2}$,$R = 8.31 \, J \, mol^{-1} K^{-1}$.

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

$A$ cylinder of volume $30 \, L$ contains oxygen at an initial gauge pressure of $15 \, atm$ and a temperature of $27^{\circ}C$. After some oxygen is withdrawn from the cylinder,the gauge pressure drops to $11 \, atm$ and its temperature drops to $17^{\circ}C$. The mass of oxygen taken out of the cylinder is approximately ........ $kg$. (Given: $R = 8.31 \, J \, mol^{-1} K^{-1}$,molar mass of $O_2 = 32 \, g/mol$ or $32 \times 10^{-3} \, kg/mol$)

$A$ vessel has $6 \text{ g}$ of hydrogen at pressure $P$ and temperature $500 \text{ K}$. $A$ small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure is $\frac{P}{2}$ and the temperature falls to $300 \text{ K}$ (in $\text{ g}$)?