Equation $(3\mathrm{.}34)$ when truncated to four terms accurately represents the volumetric data fo

methane gas at $0C$ with:

$B=-53\mathrm{.}4c{m}^3*mo{l}^{-1},C=2620c{m}^6*mo{l}^{-2},D=5000c{m}^9*mo{l}^{-3}$

$($a$)$ Use these data to prepare a plot of $Z$ vs$.P$ for methane at $0C$ from $0$ to $200$ bar.

$($b$)$ To what pressures do Eqs. $(3\mathrm{.}36)$ and $(3\mathrm{.}37)$ provide good approximations?

$Z=1+\frac{B}{V}+\frac{C}{V^2}+\frac{D}{V^3}+$dots

$Z=\frac{PV}{RT}=1+\frac{BP}{RT}$

$Z=\frac{PV}{RT}=1+\frac{B}{V}$