At $273 \ K$ temperature and $76 \ cm \ of \ Hg$ pressure,the volume of $1.786 \ g$ of a gas is $1 \ L$. The gas is likely to be .........

The use of hot air balloons for sports and meteorological observations is based on which of the following laws?

The density of acetic acid vapor at $300 \ K$ and $1 \ atm$ is $5 \ mg \ cm^{-3}$. The number of acetic acid molecules in the cluster that is formed in the gas phase is closest to

$A$ gas cylinder containing cooling gas can withstand a pressure of $14.9 \text{ atm}$. The pressure gauge of the cylinder indicates $12 \text{ atm}$ at $27 \,^oC$. Due to a sudden fire in the building,the temperature starts rising. The temperature at which the cylinder explodes is ............. $^oC$. (in $.5$)

Assuming the molar mass of air is $28.84 \, g \, mol^{-1}$,calculate the payload (lifting capacity) of a balloon of volume $10^6 \, L$ filled with $He$ at $27 \, ^\circ C$ and $1 \, atm$ pressure.

At $300 \ K$ temperature,the pressure of $2.5 \ g$ of $N_2$ gas is $4 \ bar$ and its volume is $2.5 \ L$. If the pressure becomes $10 \ bar$ at the same temperature,calculate its new volume. (in $L$)