Under what conditions does a gas behave ideally? Why?

The density of a gas is equal to ...... ($P =$ pressure,$V =$ volume,$T =$ temperature,$R =$ gas constant,$n =$ number of moles,and $M_w =$ molecular weight):

At constant pressure,the temperature of $20 \ L$ of helium gas is increased from $100 \ K$ to $300 \ K$. What will be the change in volume in $L$?

At $240.55 \ K$,for one mole of an ideal gas,a graph of $P$ (on $y$-axis) and $V^{-1}$ (on $x$-axis) gave a straight line passing through the origin. Its slope $(m)$ is $2000 \ J \ mol^{-1}$. What is the kinetic energy (in $J \ mol^{-1}$) of the ideal gas?

When an ideal gas undergoes free expansion,then:

$A$ closed tank has two compartments $A$ and $B$,both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure $1$). If the old partition is replaced by a new partition which can slide and conduct heat but does $NOT$ allow the gas to leak across (Figure $2$),the volume (in $m^3$) of the compartment $A$ after the system attains equilibrium is. . . . . . . .