Thermodynamic Properties of Methanol

8/13/2019 Thermodynamic Properties of Methanol

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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

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% 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')

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% 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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!"#$%$&"' *+

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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)

Date post:	04-Jun-2018
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Thermodynamic Properties of Methanol

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