Which of the following graphs correctly represents the variation of $\beta = - (dV/dP)/V$ with $P$ for an ideal gas at constant temperature?

$A$ gas at $27^{\circ}C$ has a volume $V$ and pressure $P$. If it is heated such that the pressure becomes double and the volume becomes triple,what is the final temperature in $^{\circ}C$?

$A$ fixed amount of gas has a volume $V$ at constant pressure. If the temperature of the gas is increased such that the $v_{rms}$ of the molecules doubles,then its new volume will be .......

$A$ gas is contained in a closed vessel. The initial temperature of the gas is $100^{\circ} C$. If the pressure of the gas is increased by $4 \%$,what is the increase in the temperature of the gas (in $^{\circ} C$)?

For $H_2, O_2$,and $He$ gases at the same temperature and pressure,the volumes are equal. Which of the following has the highest number of atoms?

The given figure represents two isobaric processes for the same mass of an ideal gas. Then: