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CHEG231-010 Chemical Engineering Thermodynamics
Semester Project: Thermodynamic Properties of Methanol
Jessica Fernandes
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alpha=(1+k.*(1-sqrt(T(j)./Tc))).^2;a_prime=-a.*k.*sqrt(alpha./(T(j).*Tc)); dPdT=(R./(V(j)-b))+(a_prime./(V(j).*(V(j)+b)+b.*(V(j)-b))); dPdV=(-R.*T (j)/(V(j)-
b).^2)+((2.*a.*alpha.*(V(j)+b))./((V(j).*(V(j)+b)+b.*(V(j)-b))).^2);
Cp_real=Cv(j)-(((T(j).*(dPdT.^2)))./(dPdV)); Cp(j)=Cp_real;end%xlabel('Temperature (K)')ylabel('Cp (J/(mol*K))')title('Constant Pressure Heat Capacity vs Temperature for
Methanol')plot(T,Cp)
hold allend
plot(T,Cp_ideal, '--') % This line corresponds the ideal gas to checkhow the behavior of the real substance is different
^$7:'* IX 4(5.' ]-,#.532 8% "*/3*'.,:'* 1$.7'./ 1(' 4*,#.-(5;
% H vs TR=8.314; % Gas constant (J/mol*K)Tc=512.6; % Methanol Critical Temperature (K)T=175.61:1000; % The temperature range goes between the triple pointand a value higher than the critical point [K]Pc=80.9*100000; % Methanol Critical Pressure (Pascal)
w=.556; % Methanol acentric factork=.37464+1.54226*w-.26992*w^2; % Kappa (Constant)
a=(.45724.*R^2.*Tc^2)./Pc; % %a(T) depends of Pc and Tc
% Specifying the desired isobars at Pr=0, Pr=0.02, Pr=0.5, Pr=1 andPr=2P = [[0] [161800] [4045000] [8090000] [16180000]]
forh=1:5forj=1:1:length(T)alpha=(1+k.*(1-sqrt(T (j)./Tc))).^2;b=(.07780.*R.*Tc)./Pc;
A=(a.*alpha.*P(h))./((R.*T(j)).^2);B=(b.*P(h))./(R.*T(j));alpha_cubic=B-1;beta_cubic=A-(3.*B.^2)-(2.*B);gamma_cubic=-(A.*B)+B.^2+B.^3;r=[1,alpha_cubic,beta_cubic,gamma_cubic]; z=roots(r);fori=1:3
if((imag (z(i))~=0))z(i)=0;end
endz=sort(z);
Zv=z(3);if(z(1)~=0)
Zl=z(1);
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!"#$%$&"' )1
elseif(z(2)~=0)Zl=z(2);
elseZl=z(3);
endCvap(j)=Zv;
V(j)=(Cvap (j).*R.*T(j))./P(h);integrand= @(V)((a.*((k^2+k)./(2.*sqrt(Tc))).*(1/T(j).^1.5))./(V.*(V+b)+b.*(V-b)));
Int=integral(integrand,Inf,V(j));
Cv_ideal=((21.15-R)+(7.09e-02.*T(j))+(2.587e-05.*T(j).^2)+(-2.852e-08.*T(j).^3));
Cv_real=((T(j).*Int))+Cv_ideal;Cv(j)=Cv_real;
alpha=(1+k.*(1-sqrt(T(j)./Tc))).^2;a_prime=-a.*k.*sqrt(alpha./(T(j).*Tc)); dPdT=(R./(V(j)-b))+(a_prime./(V(j).*(V(j)+b)+b.*(V(j)-b)));
dPdV=(-R.*T(j)/(V(j)-b).^2)+((2.*a.*alpha.*(V(j)+b))./((V(j).*(V(j)+b)+b.*(V(j)-b))).^2);
Cp_real=Cv(j)-(((T(j).*(dPdT.^2)))./(dPdV)); Cp(j)=Cp_real;enthalpy = Cp(j).*T(j)+ ((V(j)+(T(j).*dPdT./dPdV)).*P(h));H(j) = enthalpy;Hstar(j)=((21.15.*T(j))+(0.5*0.709e-01.*T(j).^2)+(0.0863e-
04.*T(j).^3)+(-0.7125e-08.*T(j).^4)); %this is to plot a graph of enthalpy of ideal gas vs. Tend
xlabel('Temperature (K)')ylabel('Molar Enthalpy (J/mol)')title('Molar Enthalpy vs Temperature for Methanol')
plot(T, H)hold allend
plot(T, Hstar, 'r')
^$7:'* MX &'*%%:'* 8% ,*/3*'.,:'* 1$.7'./ 0(' 4*,#.-(5
^$7:'* RX &'*%%:'* 8% ,*/3*'.,:'* 1$.7'./ 0(' 4*,#.-(5
%P vs T
% Declaring constants and speficic values for Methanol
R=8.314;Tc=512.6; % Methanol CriticalPc=80.9*100000; % Methanol Critical pressure to a high valueTt=175.61; % Methanol Triple Point TemperaturePt=0.1863; % Methanol Triple Ponit PressureTb=337.75; % Methanol boiling pointTm=175.55; % Methanol melting pointT=[Tt:0.01:Tc];T_subline=[100:0.01:Tc];
w=0.556; % Methanol Acentric Factor
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!"#$%$&"' *2
deltaHvap = 37440.000; % Methanol vaporization enthalpydeltaHfus = 3206.0; % Methanol fusion enthalpy
% Antoine Constants for Methanol at the temperature range (353.5 -512.63) K
Ant_A = 5.15853;
Ant_B = 1569.613;Ant_C = -34.846;
P_vap_Antoine= 10.^(Ant_A-(Ant_B./(Ant_C+T)))*10^5
P_vap_TripPoint = 10.^((Ant_A-(Ant_B./(Ant_C+Tc))))*10^5; % P(vap) atthe triple point
ClausiusClap_Pvap = exp((-deltaHvap./R).*((1./T)-(1./Tc))).*P_vap_TripPoint; %defining Clausius Clapyron forP(vaporisation)ClausiusClap_Psub = (P_vap_TripPoint).*exp((-deltaHvap./R).*((1./T_subline)-(1./Tc))); %defining Clausius Clapyron
for P(sublimation)
semilogy(T,P_vap_Antoine,'k')hold allxlabel('Temperature (K)')ylabel('Pressure (Pa)')title('P-T Phase Diagram for Methanol')semilogy(T,ClausiusClap_Pvap, 'r')semilogy(T_subline,ClausiusClap_Psub, 'c')semilogy(Tm,100000,'bo')plot(512.6,8090000,'kd')plot(175.61,0.1863,'kp')
^$7:'* NX &*-7BC(6$-%(- ]H? &'*%%:'* 8% d(5:/* 1$.7'./ 0(' 4*,#.-(5;
% Peng-Robinson EOS Pressure vs Volume for Methanol% Using one command for each isotherm:
clear all;clc ;
% For Tr=0.5
V=0.00003:0.0000001:0.5;fori = 1:1:length(V);
ifV(i)>4.58388e-05 & V(i)
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!"#$%$&"' *)
w = .556; % Methanol Acentric Factork = .37464+1.54226*w-.26992*w.^2; % kappaa1 = (1 + k*(1-sqrt(0.5))).^2;a_1 = 0.45724*(R.^2*Tc.^2/Pc)*a1;f(i)=(((R).*(t))./(V(i)-b)) - ((a_1)./(((V(i)).*(V(i) + b)) +
(b).*(V(i)-b)));
endend
% For Tr=0.6
fori = 1:1:length(V);ifV(i)>=4.82041e-05 & V(i)5.17832e-05 & V(i)5.77986e-05 & V(i)
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!"#$%$&"' **
b = 0.07780*(R*Tc/Pc);w =.556; % Methanol Acentric Factork = .37464+1.54226*w-.26992*w.^2; % kappaa2 = (1 + k*(1-sqrt(0.8))).^2;a_2 = 0.45724*(R.^2*Tc.^2/Pc)*a2;l(i)=(((R).*(t))./(V(i)-b)) - ((a_2)./(((V(i)).*(V(i) + b)) +
(b).*(V(i)-b)));endend
% For Tr=1fori = 1:1:length(V);
Pc = 80.9*100000; % Methanol Critical Pressure (Pascal)Tc = 512.6; % Methanol Critical Temperature (K)Vc = 1.18e-04; % Methanol Critical Volumet=Tc;R = 8.314; % Gas constant (J/mol*K)
b = 0.07780*(R*Tc/Pc);w =.556; %Methanol Acentric Factork = .37464+1.54226*w-.26992*w.^2; % kappaa2 = (1 + k*(1-sqrt(1))).^2;a_2 = 0.45724*(R.^2*Tc.^2/Pc)*a2;s(i)=(((R).*(t))./(V(i)-b)) - ((a_2)./(((V(i)).*(V(i) + b)) +
(b).*(V(i)-b)));end
% For Tr=2fori = 1:1:length(V);
Pc = 80.9*100000; % Methanol Critical Pressure (Pascal)Tc = 512.6; % Methanol Critical Temperature (K)Vc = 1.18e-04; % Methanol Critical Volume
t=Tc*2;R = 8.314; % Gas constant (J/mol*K)b = 0.07780*(R*Tc/Pc);
w =.556; %Methanol Acentric Factork = .37464+1.54226*w-.26992*w.^2; % kappaa2 = (1 + k*(1-sqrt(2))).^2;a_2 = 0.45724*(R.^2*Tc.^2/Pc)*a2;q(i)=(((R).*(t))./(V(i)-b)) - ((a_2)./(((V(i)).*(V(i) + b)) +
(b).*(V(i)-b)));end
figureloglog(V,f, 'r')hold all;loglog(V,g, 'g')loglog(V,h, 'c')loglog(V,l, 'b')loglog(V,s, 'k')loglog(V,q, '--')xlabel('V (m^3/mol)'), ylabel('P (Pa)'), title('P vs. V for Peng-Robinson EOS for Methanol')
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!"#$%$&"' *+
^$7:'* QX "#* G(-%,.-, ]-,'(32 +(*00$+$*-, 8% "*/3*'.,:'* 1$.7'./ 0('
4*,#.-(5;
%Mu_S versus Temperatureclear all;clc;
R=8.314; % Gas constant (J/mol*K)Tc=512.6; % Methanol Critical Temperature (K)T=175:800; % Temperature range between triple point to a value higherthan the critical point (K)Pc=80.9*100000; % Methanol Critical Pressure (Pascal)
w=.556; % Methanol acentric factork=.37464+1.54226*w-.26992*w^2; %Kappa (Constant)a=(.45724.*R^2.*Tc^2)./Pc; %a(T)values at critical temperature andpressure
% Specifying the desired isobars at Pr=0, Pr=0.02, Pr=0.5, Pr=1,Pr=1.25, Pr=1.75, and Pr=2P = [[0] [161800] [4045000] [8090000] [10112500] [14157500][16180000]]
forh=1:7forj=1:1:length(T)alpha=(1+k.*(1-sqrt(T(j)./Tc))).^2;b=(.07780.*R.*Tc)./Pc;
A=(a.*alpha.*P(h))./((R.*T(j)).^2);B=(b.*P(h))./(R.*T(j));alpha_cubic=B-1;beta_cubic=A-(3.*B.^2)-(2.*B);gamma_cubic=-(A.*B)+B.^2+B.^3;r=[1,alpha_cubic,beta_cubic,gamma_cubic]; z=roots(r);fori=1:3
if((imag(z(i))~=0))z(i)=0;end
endz=sort(z);Zv=z(3);if(z(1)~=0)Zl=z(1);
elseif(z(2)~=0)Zl=z(2);elseZl=z(3);endCvap(j)=Zv;V(j)=(Cvap(j).*R.*T(j))./P(h);integrand= @(V)
((a.*((k^2+k)./(2.*sqrt(Tc))).*(1/T(j).^1.5))./(V.*(V+b)+b.*(V-b))); Int=integral(integrand,Inf,V(j));
Cv_ideal=((21.15-R)+(7.092e-02.*T(j))+(2.587e-05.*T(j).^2)+(-2.852e-08.*T(j).^3));
Cv_real=((T(j).*Int))+Cv_ideal;Cv(j)=Cv_real;
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!"#$%$&"' *,
alpha=(1+k.*(1-sqrt(T(j)./Tc))).^2;a_prime=-a.*k.*sqrt(alpha./(T(j).*Tc)); dPdT=(R./(V(j)-b))+(a_prime./(V(j).*(V(j)+b)+b.*(V(j)-b))); dPdT_squared=dPdT.^2;dPdV=(-R.*T(j)/(V(j)-
b).^2)+((2.*a.*alpha.*(V(j)+b))./((V(j).*(V(j)+b)+b.*(V(j)-b))).^2);
Cp_real=Cv(j)-(((T(j).*dPdT_squared))./(dPdV)); Cp(j)=Cp_real;
mu_s_eq = (-T(j).*dPdT)./(Cp(j).*dPdV);Mu_S(j) = mu_s_eq;end
xlabel('Temperature (K)')ylabel('Mu_S')title('Constant Entropy Coefficient vs Temperature for Methanol')semilogy(T, Mu_S)hold allend
&8.3 ^:-+,$(-X
function[] = Pvap(P,T)R=8.314;Tc=512.6;Pc=8.09e6;
w=0.556;
k = 0.37464 + 1.54226.*w - 0.26992.*w.^2;aa = (1 + k.*(1 - (T./ Tc).^0.5)).^2;b = 0.07780 .* ((R .* Tc)./Pc);a = 0.45724 .* ((R^2 .* Tc^2)./Pc) .* aa;
A = (a.*P)./(R*T).^2;B = (b.*P)./(R*T);f = [1 B-1 A-3.*B.^2-2.*B B.^3+B.^2-A.*B];r = roots(f);
r1 = real(r);ZL = min(r1);ZV = max(r1);fL = P.*exp(ZL-1-log(ZL-B)-
(A./(2.*sqrt(2).*B)).*log((ZL+(1+sqrt(2)).*B)./(ZL+(1-sqrt(2)).*B))); fV = P.*exp(ZV-1-log(ZV-B)-
(A./(2.*sqrt(2).*B)).*log((ZV+(1+sqrt(2)).*B)./(ZV+(1-sqrt(2)).*B)));
ifabs(fV./fL-1)
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