An open-mouthed container is filled with air at $60^{\circ}C$. The container is heated to a temperature $T$ such that $1/4$ of the air escapes. The value of $T$ is ........ $^{\circ}C$.

$28\, g$ of $N_2$ gas is contained in a flask at a pressure of $10\, atm$ and at a temperature of $57^\circ C$. It is found that due to leakage in the flask,the pressure is reduced to half and the temperature is reduced to $27^\circ C$. The quantity of $N_2$ gas that leaked out is

$A$ closed hollow insulated cylinder is filled with gas at $0^{\circ} C$ and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas in one side of the piston is heated to $100^{\circ} C$. If the piston moves $5 \,cm$, the total length of the hollow cylinder is: (in $\,cm$)

$A$ sample of an ideal gas occupies a volume $V$ at a pressure $P$ and absolute temperature $T,$ the mass of each molecule is $m.$ The expression for the density of gas is ($k =$ Boltzmann's constant)

The average force applied on the wall of a closed container depends as $T^{x}$ where $T$ is the temperature of an ideal gas. The value of $x$ is

When the temperature of a gas at constant volume is increased by $5^{\circ}C$,its pressure increases by $0.5\%$ of its initial value. The initial temperature of the gas is..... $K$.