What are the values of $Z$ for $CO_2, CH_4$,and $O_2$ at $200 \ bar$ and $900 \ bar$ pressure?

When helium is allowed to expand into vacuum,a heating effect is observed. The reason for this is that

In the given $pV \to V$ graph for gases at constant temperature,what kind of deviation will be observed for $H_2, He, CO, CH_4$?

The $P$ vs $V$ graph is plotted for $1$ $mole$ of a hypothetical gas. Based on the given isotherms at $200 \ K$ and $300 \ K$,determine the range of $\frac{a}{b}$ for this gas in $atm-L \ mole^{-1}$. [Given: $R = 0.08 \ atm-L \ mole^{-1} \ K^{-1}$]

Explain the effect of high pressure and low temperature on the validity of Boyle's law.

Derive the van der Waals equation.