Which of the following shows the correct relationship between the pressure $P$ and density $\rho$ of an ideal gas at constant temperature?

Pressure of an ideal gas,contained in a closed vessel,is increased by $0.4 \%$ when heated by $1^{\circ} C$. Its initial temperature must be

The tyre of a motor car contains air at $15^{\circ} C$. If the temperature increases to $35^{\circ} C$, the approximate percentage increase in pressure is (ignore the expansion of the tyre).

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

Oxygen gas is filled in a container of volume $20 \, L$ at a pressure of $2.5 \times 10^5 \, N \, m^{-2}$. Find the mass of the oxygen gas in the container. The temperature of the oxygen in the container is $27 \, ^\circ C$,the molar mass of oxygen is $32 \, g \, mol^{-1}$,and $R = 8.31 \, J \, mol^{-1} K^{-1}$.

If the pressure of a gas contained in a closed vessel is increased by $0.4\%$ when heated by $1\,^{\circ}C$,the initial temperature must be