$A$ 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

$A$ given sample of an ideal gas occupies a volume $V$ at a pressure $P$ and absolute temperature $T.$ The mass of each molecule of the gas is $m.$ Which of the following gives the density of the gas $?$

An ideal gas at temperature $T$, pressure $p$ occupies a volume $V$. If its temperature is halved and pressure doubled, what is its new volume?

$A$ gas at the temperature $250\,K$ is contained in a closed vessel. If the gas is heated through $1\,K,$ then the percentage increase in its pressure will be ...... $\%$

The pressure and temperature of an ideal gas in a closed vessel are $720 \, kPa$ and $40^\circ C$ respectively. If $\frac{1}{4}^{th}$ of the gas is released from the vessel and the temperature of the remaining gas is raised to $353^\circ C$,the final pressure of the gas is ....... $kPa$.

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 .......... $g$.