An ideal gas is expanding such that $PT^2 = \text{constant}$. The coefficient of volume expansion of the gas is

$A$ tyre of a vehicle is filled with air having pressure $270 \text{ kPa}$ at $27^{\circ}C$. The air pressure in the tyre when the temperature increases to $37^{\circ}C$ is (in $\text{ kPa}$)

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 $^{\circ}C$?

$A$ vertical closed cylinder is separated into two parts by a frictionless piston of mass $m$ and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is $l_1,$ and that below the piston is $l_2,$ such that $l_1 > l_2.$ Each part of the cylinder contains $n$ moles of an ideal gas at equal temperature $T.$ If the piston is stationary,its mass $m$ will be given by: ($R$ is the universal gas constant and $g$ is the acceleration due to gravity)

The graph shows the $PV$ vs $P$ plot for different gases at a constant temperature. Which graph represents an ideal gas?

$A$ vessel containing $5 \, L$ of a gas at $0.8 \, Pa$ pressure is connected to an evacuated vessel of volume $3 \, L$. The resultant pressure inside will be ...... $Pa$ (assuming the whole system to be isolated).