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+// Y.V.C.Rao ,1997.Chemical Engineering Thermodynamics.Universities Press,Hyderabad,India.

+

+//Chapter-9,Example 12,Page 335

+//Title: Molar volume of mixture using van der Waals equation of state

+//================================================================================================================

+clear 

+clc

+

+//INPUT

+T=600;//temperature of the equimolar n-butane and n-octane mixture in K

+P=16;//pressure of the equimolar n-butane and n-octane mixture in bar

+a_m=2.4405;//van der Waals constant for the mixture as determined in Example 9.8 in Pa(m^3/mol)^2

+b_m=0.1767*10^-3;//van der Waals constant for the mixture as determined in Example 9.8 in m^3/mol

+R=8.314;//universal gas constant in J/molK

+

+//CALCULATION

+//The problem is solved by using the Cardan's method

+A=(a_m*P*10^5)/(R*T)^2;//calculation of A to determine alpha,beeta and gaamma by using Eq.(3.25)

+B=(b_m*P*10^5)/(R*T);//calculation of B to determine alpha,beeta and gaamma by using Eq.(3.26)

+alpha=-1-B;//calculation of alpha for van der Waals equation of state using Table (3.2)

+beeta=A;//calculation of beeta for van der Waals equation of state using Table (3.2)

+gaamma=-(A*B);//calculation of gaamma for van der Waals equation of state using Table (3.2)

+p=beeta-((alpha^2)/3);//calculation of p to determine the roots of the cubic equaton using Eq.(3.29)

+q=((2*alpha^3)/27)-((alpha*beeta)/3)+gaamma;//calculation of q to determine the roots of the cubic equaton using Eq.(3.30)

+D=(((q)^2)/4)+(((p)^3)/27);//calculation of D to determine the nature of roots using Eq.(3.31)

+

+if D>0 then

+        Z=(((-(q)/2)+(sqrt(D)))^(1/3))+(((-(q)/2)-(sqrt(D)))^(1/3))-(alpha/3);//One real root given by  Eq.(3.32)

+else if D==0 then

+        Z1=((-2*(q/2))^(1/3))-(alpha/3);//Three real roots and two equal given by Eq.(3.33)

+        Z2=((q/2)^(1/3))-(alpha/3);

+        Z3=((q/2)^(1/3))-(alpha/3);

+        Za=[Z1 Z2 Z3];

+        Z=max(Za);

+    else

+        r=sqrt((-(p^3)/27));//calculation of r using Eq.(3.38)

+        theta=acos((-(q)/2)*(1/r));//calculation of theta in radians using Eq.(3.37)

+        Z1=(2*(r^(1/3))*cos(theta/3))-(alpha/3);

+        Z2=(2*(r^(1/3))*cos(((2*%pi)+theta)/3))-(alpha/3);//Three unequal real roots given by Eqs.(3.34,3.35 and 3.36)

+        Z3=(2*(r^(1/3))*cos(((4*%pi)+theta)/3))-(alpha/3);

+        Za=[Z1 Z2 Z3];

+        Z=max(Za);

+    end

+end

+vm=(Z*R*T)/(P*10^5);//calculation of the molar volume of the equimolar mixture in m^3/mol

+

+//OUTPUT

+mprintf("\n The molar volume of an equimolar mixture of n-butane and n-octane at 600K and 16bar found using the van der Waals equation of state = %e m^3/mol\n",vm);

+

+//===============================================END OF PROGRAM===================================================

+// DISCLAIMER: VALUE OF Z COMPUTED IN PROGRAM IS NOT AS THAT REPORTED IN THE TEXTBOOK. HOWEVER, VALUES OF ALL OTHER PERTINENT VARIABLES A, B, alpha, beeta, p, q etc. AGREE WELL WITH THE TEXTBOOK ANSWER. COMPUTATION WAS ALSO VERIFIED MANUALLY AND GAVE THE ANSWER AS COMPUTED IN PROGRAM. ONE POSSIBLE REASON FOR DEVIATION COULD BE ROUND OFF ERROR.