Two different isotherms representing the relationship between pressure $p$ and volume $V$ at a given temperature for the same ideal gas are shown for masses $m_1$ and $m_2$ of the gas respectively in the figure given. Then:

At the top of a mountain,a thermometer reads $7^{\circ}C$ and a barometer reads $70 \, cm$ of $Hg$. At the bottom of the mountain,these read $27^{\circ}C$ and $76 \, cm$ of $Hg$ respectively. The ratio of the density of air at the top to that at the bottom is

When the temperature of a gas in a closed vessel is increased by $1 \ ^\circ C$,its pressure increases by $0.4 \ \%$. The initial temperature of the gas is:

In a process,the pressure of an ideal gas varies with volume as $P = \frac{a}{1 + (V/b)^2}$,where $a$ and $b$ are constants. What is the temperature of the gas when the volume of $1$ mole of the gas is $V = b$?

Air is filled at $60^{\circ} C$ in a vessel of open mouth. The vessel is heated to a temperature $t^{\circ} C$ so that $\frac{1}{4}$th of the air escapes from the vessel. Assuming air as an ideal gas and the volume of the vessel remains constant, the value of '$t$' is: (in $^{\circ} C$)

The temperature of a gas at pressure $P$ and volume $V$ is $27^{\circ}C$. Keeping its volume constant,if its temperature is raised to $927^{\circ}C$,then its pressure will be (in $P$)