An ideal gas has an initial pressure of $3$ pressure units and an initial volume of $4$ volume units. The table gives the final pressure and volume of the gas (in those same units) in four processes. Which processes start and end on the same isotherm?

$A$. Process $A$	$P=5, V=7$
$B$. Process $B$	$P=4, V=6$
$C$. Process $C$	$P=12, V=1$
$D$. Process $D$	$P=6, V=3$

$A$ 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 relationship between pressure and the density of a gas expressed by Boyle's law,$P = K\rho$,holds true:

If an ideal gas has volume $V$ at $27^{\circ}C$ and it is heated at a constant pressure so that its volume becomes $1.5V$,then the value of the final temperature will be ....... $^{\circ}C$.

Write the ideal gas equation. What is the basis of the absolute temperature scale?

$A$ 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 .......