Question

1) ) Cubic equations of state can be used to establish the pressure(P)-volume(V)-temperature (T) relationship of fluids. A typical one is called Redlich/Kwong equation of state and is in the following form: R T where a and b are fluid specific parameters and R is the gas constant 83.14 cm bar/mol.K When this equation is solved for volume (V) the largest root yield the vapor-phase volume whereas the smallest root yields the liquid-phase volume. Use the bisection method calculate the smallest root of the equation, in order to obtain the liquid-phase volume of butane at 350 K and 9.46 bar for which a- 2.9x108 and b 807,

I need to solve this using matlab.

Answer 1

Code: MainV.m

clc
clear
%%initial guess
xl = 1;
xu = 3600;

fl = funVol(xl);
fu = funVol(xu);

%check if signs of fx and fu are different
if (fl*fu > 0)
error('Initial guesses should have different signs');
end
%%iterative solution using bisection rule
maxIter = 100;
tolX = 1e-6;
for i = 1:maxIter
err = abs(xl - xu);
xNew = (xl + xu)/2;
fNew = funVol(xNew);
if(fl*fNew > 0)
xl = xNew;
fl = fNew;
else
xu = xNew;
fu = fNew;
end
if (abs(err) < tolX)
break;
end
end
disp("Smallest root V0 = "+num2str(xNew));

Code: funVol.m

function fvol = funVol(V)
R = 83.14;
T = 350;
P = 9.46;
a = 2.9*10^8;
b = 807;
fvol = V^3 - R*T/P *V^2 - (b^2 + b*R*T/P - a/(P*sqrt(T)))*V - a*b /(P*sqrt(T));

end

Output:

Command Window Smallest root VO 3594.2944 fx >>