A$)$ Given the following temperature and pressures for $C{O}_2,$ plot the isotherm on a $P-V$ diagram,

indicating the phase envelop as well. Use the Peng$-$Robinson Equation of State to do this.

Compound: $C{O}_2,$ Temperature: $250$K$,$ Pressures of $0\mathrm{.}0010,0\mathrm{.}10,1\mathrm{.}0,1\mathrm{.}7608,2\mathrm{.}0,3\mathrm{.}0,10,20,30,60,$

$100$Mpa.

B$)$ When cubic equations of state give three real roots for the compressibility factor, usually the

smallest root is the liquid root and the largest is the vapor root. However, the Peng$-$Robinson EOS

can give real roots at high pressure that differ from this pattern. To study this behavior, tabulate all

of the roots for the specified gas and pressures given in part a$).$

i$)$ As the highest pressures are approached the given temperature, is the fluid a liquid or a vapor?

ii$)$ Which real root $($smallest$,$ middle or largest$)$ represents this phase at the highest pressure?

iii$)$ What are the compressibility factor values at the specified pressures?

Please show your work for problem $2$ wither with images of the excel sheet for each solution that you are discussing or

the Matlab output.