$A$ given sample of an ideal gas occupies a volume $V$ at a pressure $P$ and absolute temperature $T.$ The mass of each molecule of the gas is $m.$ Which of the following gives the density of the gas $?$

The figure shows the volume versus temperature graph for the same mass of an ideal gas corresponding to two different pressures $P_1$ and $P_2$. Then,

An ideal gas is initially at temperature $T$ and volume $V.$ Its volume is increased by $\Delta V$ due to an increase in temperature $\Delta T,$ pressure remaining constant. The quantity $\delta = \Delta V / (V \Delta T)$ varies with temperature as

Two identical glass bulbs are connected by a thin glass tube. The system is filled with gas at $0^{\circ}C$. If one bulb is placed in ice and the other in hot water,the pressure of the gas becomes $1.5$ times the initial pressure. What is the temperature of the hot water in $^{\circ}C$?

The gas which obeys Boyle's law for the maximum range of temperature is

$A$ perfect gas at $27^{\circ} C$ is heated at constant pressure so as to double its volume. The increase in temperature of the gas will be (in $^{\circ} C$)