In the equation $PV = KT$,the value of $K$ depends on which factors?

Which one of the following graphs represents the behavior of an ideal gas at a constant temperature?

$A$ 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)

At $0\,^{\circ}\text{C}$,the value of the density of a fixed mass of an ideal gas divided by its pressure is $x$. At $100\,^{\circ}\text{C}$,this value will be

For an ideal gas undergoing a constant temperature process (isothermal process),what is the nature of the graph between pressure $(P)$ and $\frac{1}{V}$ (where $V$ is volume)?

The gas in a vessel is subjected to a pressure of $20 \ atm$ at a temperature of $27^{\circ}C$. If one-half of the gas is released from the vessel and the temperature of the remaining gas is raised by $50^{\circ}C$,the final pressure of the gas in the vessel is ....... $atm$.