If the compressibility factor $(Z)$ of a real gas is $1.05$ at $STP$,what is the molar volume of the real gas (in $dm^3$)?

For $1$ mol of a real gas kept at constant temperature $T$,the graph of $PV$ vs $P$ intersects the $PV$ axis at $20$. Hence,the temperature $T$ is ($R$ = universal gas constant).

$A$ gas has a compressibility factor of $0.5$ and a molar volume of $0.4 \ dm^3 \ mol^{-1}$ at a temperature of $800 \ K$ and pressure $x \ atm$. If it shows ideal gas behaviour at the same temperature and pressure,the molar volume will be $y \ dm^3 \ mol^{-1}$. The value of $x / y$ is . . . . . .
[Use: Gas constant,$R = 8 \times 10^{-2} \ L \ atm \ K^{-1} \ mol^{-1}$ ]

The compressibility factor $(Z)$ of a gas at moderate pressure is:

When helium gas is allowed to expand into vacuum, a heating effect is observed. The reason for this is (assume $He$ as a non-ideal gas):

What are the ideal pressure and volume of a real gas?