Problem $1$

Find out the molar volume of the water vapor $($gaseous phase$)$ using Peng$-$Robinson equation of state equation at $P=3\mathrm{.}5$MPa and $T=505K$ Use the ideal gas equation for guess.

PREOS:

$P=\frac{RT}{V-b}-\frac{a}{V^2+2bV-b^2}$

$a=\frac{0\mathrm{.}45724R^2{T}_C^2}{P_C}$

$b=\frac{0\mathrm{.}07780R{T}_C}{P_C}$

$=(1+(1-T_r^{0\mathrm{.}5}){)}^2$

$=0\mathrm{.}37464+1\mathrm{.}54226-0\mathrm{.}26992{}^2$

$T_r=\frac{T}{T_c}$

$\backslash$table$[[$Constant$,$Value,Unit$],[R,8\mathrm{.}314,c{m}^{3}MP\frac{a}{\text{m}\text{o}\text{l}\text{K}}$