Find the temperature $($in degrees Celsius of saturated steam at a pressure P $=3$ MPa and

specific volume v $=0\mathrm{.}066667$ m$\text{'}/$kg using the Peng$-$Robinson equation of state shown

below. Solve the equation using your Modified Regula Falsi program.

RT

P$=$

a

Dv$+$b$)+$b$(1-$ b$)$

where

aoR?T$?$

a $=$

boRIc b $=$

Pc

a$0=0\mathrm{.}45724[1+$ F$(1-/$Tr$)?$

f $($w$)=0\mathrm{.}37464+$ @ $(1\mathrm{.}54226-0\mathrm{.}26992$ w

bo $=0\mathrm{.}0778$

Ir $=$ T$/$Tc

Note that:

$1)$ Absolute temperature must be used $($K $=$ C $+273\mathrm{.}15).$

$2)$ The gas constant R $=$ R$/$M where the universal gas constant R $=8\mathrm{.}31434$

kJ$/$kmol$-\backslash$deg K and the molecular weight of water is M $=18\mathrm{.}01528$ kg$/$kmol$.$

$3)$ The critical constants for steam are Pc $=22\mathrm{.}064$ MPa and Ic $=373\mathrm{.}95\backslash$deg C$.$

Please submit the following:

$1)$ A plot which shows the location all real roots T $($K$)$ of the equation for the given values of P and v$.$

$2)$ A flow chart of the Modified Regula Falsi algorithm.

$3)$ A listing of your Matlab main program and all function programs used.

$4)$ Printed output from your program showing the appropriate root T $($K$)$ computed to an accuracy of at least $8$ significant figures.

$5)$ The calculated value of the temperature T $($in degrees Celsius$)$ using the Peng$-$Robinson equation of state, the ideal gas equation of state, and the relative error of each based on the value of the saturation temperature at $3$ MPa reported in steam tables $(233\mathrm{.}85\backslash$deg C$).$ Present at least $5$ significant figures in your results.