$A$ vessel that can withstand a pressure of $100 \,atm$ is filled with hydrogen at $27^{\circ} C$ up to a pressure of $20 \,atm$. If the vessel is heated, then the temperature at which it explodes is (in $\,K$)

The temperature of an open room of volume $30\ m^3$ increases from $17^\circ C$ to $27^\circ C$ due to sunshine. The atmospheric pressure in the room remains $1 \times 10^5\ Pa$. If $n_i$ and $n_f$ are the number of molecules in the room before and after heating,then $n_f - n_i$ will be:

An electron tube was sealed off during manufacture at a pressure of $1.2 \times 10^{-7} \text{ mm}$ of mercury at $27^{\circ}C$. Its volume is $100 \text{ cm}^3$. The number of molecules that remain in the tube is

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?

The $PV$ versus $T$ graph for equal masses of $H_2, He$,and $O_2$ is shown in the figure. Choose the correct alternative:

The temperature of a gas at $-173^{\circ} C$ is $1 \text{ atm}$ at constant volume. Up to what temperature should the gas be heated so that the pressure becomes $2 \text{ atm}$ (in $^{\circ} C$)?