With the explicit expressions - ideal gas

kB=1.380649 (10^(-23));(*J/K*)
h=6.62607015 (10^(-34)); (*J/Hz*)
Da=1.66053906660 (10^(-27));(*kg*)

κnum=100;κmin=0.5;κmax=2;Ratios4κ=Table[{},{i,1,κnum+1}];

For[j=1,j≤κnum+1,j++,
κ=κmin+(j-1) (κmax-κmin)/κnum; (*=m2/m1*) 
u=0;
m2=10 Da;(*mass of a molecule*)
(*mixture state variables*)
ρ=1; (*kg/(m^3)*)
u=0 (10^3); (*kg m/s*) 
(*set either energy or temperature*)
e= (3/2) kB 300((ρ/m2))+(1/2)((u^2)/ρ); (*J/(m^3)*)(*some reasonable estimate of total mixture energy; Note that with u=0 we have e=ϵ, that is total mixture energy is equal to internal mixture energy*)
(*T=300;(*K*) *)
rel26=((κ )^(5/2 κ))(m2^(4 (1-κ))) ((ρ1)^κ)(((4 (π/3) ((e-((u^2)/(2 ρ)))/((h^2) (κ ρ1+ρ-ρ1)))))^(3/2 (1-κ)));
rel24=((2 e (ρ^2)+(u^2) ((κ^(-1))-1)(ρ-ρ1))/(2 ρ (ρ1+(κ^(-1))(ρ-ρ1))))((ρ1)/ρ);
rel23=((ρ1)/ρ) u;
ρ1sol=FindRoot[ρ-ρ1==rel26,{ρ1,0.5 ρ}]//Flatten;
e1sol=FindRoot[e1==rel24/.ρ1sol,{e1,0.5 e}]//Flatten;
u1sol=FindRoot[u1==((ρ1)/ρ)u/.ρ1sol,{u1,0.5 u}]//Flatten;
ρ2sol={ρ2->((ρ-ρ1)/.ρ1sol)};
e2sol={e2->(e-e1/.e1sol)};
u2sol={u2->(((ρ2)/ρ) u/.ρ2sol)};
s1sol={s1->(kB ((ρ1)/m1)((5/2)+Log[(m1/(ρ1))(((((4 π m1)/(3 (h^2))) ((e1-((u1^2)/(2 ρ1)))/(ρ1/m1))))^(3/2))])/.m1->m2 (κ^(-1))/.ρ1sol/.u1sol/.e1sol)};
s2sol={s2->(kB ((ρ2)/m2)((5/2)+Log[(m2/(ρ2))(((((4 π m2)/(3 (h^2))) ((e2-((u2^2)/(2 ρ2)))/(ρ2/m2))))^(3/2))])/.ρ2sol/.u2sol/.e2sol)};
ρstar=-(kB/m1)Log[((ρ1)/m1)]+(3/2)(kB/m1)Log[((4 π m1)/(3 (h^2))) (m1/(ρ1))(e1-((u1^2)/(2 ρ1)))]+(3/2)(kB/m1) (1/(e1-((u1^2)/(2 ρ1))))((u1^2)/(2 ρ1))/.m1->m2 (κ^(-1))/.ρ1sol/.u1sol/.e1sol;
estar=D[(kB ((ρ1)/m1)((5/2)+Log[(m1/(ρ1))(((((4 π m1)/(3 (h^2))) ((e1-((u1^2)/(2 ρ1)))/(ρ1/m1))))^(3/2))])),e1]/.m1->m2 (κ^(-1))/.ρ1sol/.u1sol/.e1sol;
p=(-e+ρ μ+T s)/.μ->(-ρstar T)/.T->1/estar/.s->s1+s2/.ρ1sol/.e1sol/.s1sol/.s2sol;
p1=-e1+ρ1 μ+T s1/.μ->(-ρstar T)/.T->1/estar/.e1sol/.ρ1sol/.s1sol;
p2=-e2+ρ2 μ+T s2/.μ->(-ρstar T)/.T->1/estar/.e2sol/.ρ2sol/.s2sol;
Ratios4κ[[j]]={κ,Chop[ρ1/ρ/.ρ1sol],Chop[(((ρ1)/ρ)e/e1)/.ρ1sol/.e1sol],
Chop[(((ρ1)/ρ)s/s1)/.s->s1+s2/.ρ1sol/.s1sol/.s2sol],
Chop[((((ρ1)/ρ)e-e1)-T(((ρ1)/ρ)s-s1))/(((ρ1)/ρ)p)/.s->s1+s2/.ρ1sol/.e1sol/.s1sol/.s2sol],Chop[(ρ1)/.ρ1sol],Chop[(ρ2)/.ρ2sol],Chop[(e1)/.e1sol],Chop[(e2)/.e2sol],Chop[(s1)/.s1sol],Chop[(s2)/.s2sol],Chop[p],Chop[p1],Chop[p2],Chop[estar]}];

Clear[κ,j,p,p1,p2,estar];

ListPlot[{Table[{Ratios4κ[[j,1]],Chop[((((ρ1)/ρ)(e1+e2)-e1)-(1/estar)(((ρ1)/ρ)(s1+s2)-s1))/(((ρ1)/ρ)p)/.ρ1->Ratios4κ[[j,6]]/.ρ2->Ratios4κ[[j,7]]/.e1->Ratios4κ[[j,8]]/.e2->Ratios4κ[[j,9]]/.s1->Ratios4κ[[j,10]]/.s2->Ratios4κ[[j,11]]/.p->Ratios4κ[[j,12]]/.p1->Ratios4κ[[j,13]]/.p2->Ratios4κ[[j,14]]/.estar->Ratios4κ[[j,15]],(10^(-8))]},{j,1,κnum+1}],Table[{Ratios4κ[[j]][[1]],Chop[((((ρ2)/ρ)(e1+e2)-e2)-(1/estar)(((ρ2)/ρ)(s1+s2)-s2))/(((ρ2)/ρ)p)/.ρ1->Ratios4κ[[j,6]]/.ρ2->Ratios4κ[[j,7]]/.e1->Ratios4κ[[j,8]]/.e2->Ratios4κ[[j,9]]/.s1->Ratios4κ[[j,10]]/.s2->Ratios4κ[[j,11]]/.p->Ratios4κ[[j,12]]/.p1->Ratios4κ[[j,13]]/.p2->Ratios4κ[[j,14]]/.estar->Ratios4κ[[j,15]],(10^(-8))]},{j,1,κnum+1}]},AxesStyle -> Thickness[0.0025],PlotTheme->{"Monochrome"},LabelStyle->{FontSize->16,Black},AxesLabel -> {Style["κ"(*"\kappa"*), FontFamily->"Times",FontSize -> 20]}]

index 1 is denoted with circles, index 2 with triangles

Testing Dalton’s law of partial pressures, distribution according to ((Subscript[p, α])-(Subscript[x, α]) p)/((Subscript[x, α]) p)

ListPlot[{Table[{Ratios4κ[[j,1]],Chop[(p1-((ρ1)/(ρ1+(κ^(-1))ρ2)) p)/(((ρ1)/(ρ1+(κ^(-1))ρ2))p)/.κ->Ratios4κ[[j,1]]/.ρ1->Ratios4κ[[j,6]]/.ρ2->Ratios4κ[[j,7]]/.e1->Ratios4κ[[j,8]]/.e2->Ratios4κ[[j,9]]/.s1->Ratios4κ[[j,10]]/.s2->Ratios4κ[[j,11]]/.p->Ratios4κ[[j,12]]/.p1->Ratios4κ[[j,13]]/.p2->Ratios4κ[[j,14]]/.estar->Ratios4κ[[j,15]],(10^(-8))]},{j,1,κnum+1}],Table[{Ratios4κ[[j,1]],Chop[(p2-(((κ^(-1))ρ2)/(ρ1+(κ^(-1))ρ2)) p)/((((κ^(-1))ρ2)/(ρ1+(κ^(-1))ρ2))p)/.κ->Ratios4κ[[j,1]]/.ρ1->Ratios4κ[[j,6]]/.ρ2->Ratios4κ[[j,7]]/.e1->Ratios4κ[[j,8]]/.e2->Ratios4κ[[j,9]]/.s1->Ratios4κ[[j,10]]/.s2->Ratios4κ[[j,11]]/.p->Ratios4κ[[j,12]]/.p1->Ratios4κ[[j,13]]/.p2->Ratios4κ[[j,14]]/.estar->Ratios4κ[[j,15]],(10^(-8))]},{j,1,κnum+1}]},AxesStyle -> Thickness[0.0025],PlotTheme->{"Monochrome"},LabelStyle->{FontSize->16,Black},AxesLabel -> {Style["κ"(*"\kappa"*), FontFamily->"Times",FontSize -> 20]},PlotRange->{-0.01,0.01}]

(numerically) Without the explicit expressions - ideal gas

s1=kB ((ρ1)/m1) ((5/2)+Log[(m1/(ρ1))(((((4 π m1)/(3 (h^2)))((e1-((u1^2)/(2 ρ1)))/(ρ1/m1))))^(3/2))]);
s2=kB ((ρ2)/m2) ((5/2)+Log[(m2/(ρ2))(((((4 π m2)/(3 (h^2)))((e2-((u2^2)/(2 ρ2)))/(ρ2/m2))))^(3/2))]);
s=s1+s2;

FirstMEstep={D[s,ρ1]==ρstar,D[s,ρ2]==ρstar,D[s,u1]==ustar,D[s,u2]==ustar,D[s,e1]==estar,D[s,e2]==estar}//Simplify;

instead of the second step, we use the upscaling mapping

Projections={ρ==ρ1+ρ2,u==u1+u2,e==e1+e2};

kB=1.380649 (10^(-23));(*J/K*)
h=6.62607015 (10^(-34)); (*J/Hz*)
Da=1.66053906660 (10^(-27));(*kg*)

With a prescribed energy:

κnum=100;κmin=0.5;κmax=2;Ratios4κ=Table[{},{i,1,κnum+1}];Clear[j,p,p1,p2,e,T,estar,κ,m1,m2];
For[j=1,j≤κnum+1,j++,
κ=κmin+(j-1) (κmax-κmin)/κnum;
m2=10 Da;(*mass of a molecule*)
m1=m2/κ; (*κ=m2/m1*) 
(*mixture state variables*)
ρ=1; (*kg/(m^3)*)
u=0 (10^3); (*kg m/s*)
e= (3/2) kB 300((ρ/m2))+(1/2)((u^2)/ρ); (*J/(m^3)*)(*some reasonable estimate of total mixture energy from a prescribed temperature; again, internal and total are equal*)
numEstimate=Chop[FindRoot[FirstMEstep⋃Projections,{{ρ1,ρ(1.5 (κ-0.45))},{ρ2,ρ(1-(1.5 (κ-0.45)))},{u1,u/2},{u2,u/2},{e1,e/2},{e2,e/2},{ρstar,(10^3)},{ustar,1},{estar,1/300}}]];
p=(-e+ρ μ+T s)/.μ->(-ρstar T)/.T->1/estar/.numEstimate;
p1=-e1+ρ1 μ+T s1/.μ->(-ρstar T)/.T->1/estar/.numEstimate;
p2=-e2+ρ2 μ+T s2/.μ->(-ρstar T)/.T->1/estar/.numEstimate;
Ratios4κ[[j]]={κ,ρ1/.numEstimate,ρ2/.numEstimate,u1/.numEstimate,u2/.numEstimate,e1/.numEstimate,e2/.numEstimate,p,p1,p2,1/estar/.numEstimate}];

Clear[j,p,p1,p2,m1,κ,estar]

ListPlot[Table[{Ratios4κ[[j,1]],((((ρ1)/ρ)(e1+e2)-e1)-T(((ρ1)/ρ)s-s1))/(((ρ1)/ρ) p)/.m1->m2/Ratios4κ[[j,1]]/.T->1/estar/.ρ1->Ratios4κ[[j,2]]/.ρ2->Ratios4κ[[j,3]]/.u1->Ratios4κ[[j,4]]/.u2->Ratios4κ[[j,5]]/.e1->Ratios4κ[[j,6]]/.e2->Ratios4κ[[j,7]]/.p->Ratios4κ[[j,8]] /.estar->Ratios4κ[[j,11]]},{j,1,κnum+1}],AxesLabel->{"κ","((((ρ1)/ρ)e-e1)-T(((ρ1)/ρ)s-s1))/(((ρ1)/ρ)p) ratio"}(*,MaxPlotPoints->60*)]
ListPlot[Table[{Ratios4κ[[j,1]],((((ρ2)/ρ)(e1+e2)-e2)-T(((ρ2)/ρ)s-s2))/(((ρ2)/ρ) p)/.m1->m2/Ratios4κ[[j,1]]/.T->1/estar/.ρ1->Ratios4κ[[j,2]]/.ρ2->Ratios4κ[[j,3]]/.u1->Ratios4κ[[j,4]]/.u2->Ratios4κ[[j,5]]/.e1->Ratios4κ[[j,6]]/.e2->Ratios4κ[[j,7]]/.p->Ratios4κ[[j,8]] /.estar->Ratios4κ[[j,11]]},{j,1,κnum+1}],AxesLabel->{"κ","((((ρ2)/ρ)e-e2)-T(((ρ2)/ρ)s-s2))/(((ρ2)/ρ)p) ratio"}(*,MaxPlotPoints->60*)]
ListPlot[Table[{Ratios4κ[[j,1]],(p1-((ρ1/m1)/(ρ1/m1+ρ2/m2))p)/(((ρ1/m1)/(ρ1/m1+ρ2/m2)) p)/.m1->m2/Ratios4κ[[j,1]]/.ρ1->Ratios4κ[[j,2]]/.ρ2->Ratios4κ[[j,3]]/.u1->Ratios4κ[[j,4]]/.u2->Ratios4κ[[j,5]]/.e1->Ratios4κ[[j,6]]/.e2->Ratios4κ[[j,7]]/.p->Ratios4κ[[j,8]]/.p1->Ratios4κ[[j,9]]/.p2->Ratios4κ[[j,10]]},{j,1,κnum+1}],AxesLabel->{"κ","\!\(TraditionalForm\`\((\*SubscriptBox[\(p\), \(1\)] - \*SubscriptBox[\(x\), \(1\)]\\ p)\)/\((\*SubscriptBox[\(x\), \(1\)] p)\)\)"}(*,MaxPlotPoints->60*)]
ListPlot[Table[{Ratios4κ[[j,1]],(p2-((ρ2/m2)/(ρ1/m1+ρ2/m2))p)/(((ρ2/m2)/(ρ1/m1+ρ2/m2)) p)/.m1->m2/Ratios4κ[[j,1]]/.ρ1->Ratios4κ[[j,2]]/.ρ2->Ratios4κ[[j,3]]/.u1->Ratios4κ[[j,4]]/.u2->Ratios4κ[[j,5]]/.e1->Ratios4κ[[j,6]]/.e2->Ratios4κ[[j,7]]/.p->Ratios4κ[[j,8]]/.p1->Ratios4κ[[j,9]]/.p2->Ratios4κ[[j,10]]},{j,1,κnum+1}],AxesLabel->{"κ","\!\(TraditionalForm\`\((\*SubscriptBox[\(p\), \(2\)] - \*SubscriptBox[\(x\), \(2\)]\\ p)\)/\((\*SubscriptBox[\(x\), \(2\)] p)\)\)"}(*,MaxPlotPoints->60*)]

With a prescribed temperature:

κnum=100;κmin=0.5;κmax=2;Ratios4κ=Table[{},{i,1,κnum+1}];Clear[j,p,p1,p2,e,T,estar,κ,m1,m2];
For[j=1,j≤κnum+1,j++,
κ=κmin+(j-1) (κmax-κmin)/κnum;
m2=10 Da;(*mol mass*)
m1=m2/κ; (*κ=m2/m1*) 
(*mixture state variables*)
ρ=1; (*kg/(m^3)*)
u=0 (10^3); (*kg m/s*)
T=300; (*K*)
estar=1/T;
eestimate=(3/2)kB/estar((ρ/((m1+m2)/2)))+(1/2)((u^2)/ρ); (*with u=0, total=internal*)
numEstimate=Chop[FindRoot[FirstMEstep⋃Projections,{{ρ1,ρ/2},{ρ2,ρ/2},{u1,u/2},{u2,u/2},{e1,eestimate/2},{e2,eestimate/2},{ρstar,(10^3)},{ustar,1},{e,eestimate}}]];
p=(-e+ρ μ+T s)/.μ->(-ρstar T)/.numEstimate;
p1=-e1+ρ1 μ+T s1/.μ->(-ρstar T)/.numEstimate;
p2=-e2+ρ2 μ+T s2/.μ->(-ρstar T)/.numEstimate;
Ratios4κ[[j]]={κ,ρ1/.numEstimate,ρ2/.numEstimate,u1/.numEstimate,u2/.numEstimate,e1/.numEstimate,e2/.numEstimate,p,p1,p2}];

Clear[j,p,p1,p2,m1,κ,estar]

ListPlot[Table[{Ratios4κ[[j,1]],((((ρ1)/ρ)(e1+e2)-e1)-T(((ρ1)/ρ)s-s1))/(((ρ1)/ρ) p)/.m1->m2/Ratios4κ[[j,1]]/.ρ1->Ratios4κ[[j,2]]/.ρ2->Ratios4κ[[j,3]]/.u1->Ratios4κ[[j,4]]/.u2->Ratios4κ[[j,5]]/.e1->Ratios4κ[[j,6]]/.e2->Ratios4κ[[j,7]]/.p->Ratios4κ[[j,8]] },{j,1,κnum+1}],AxesLabel->{"κ","((((ρ1)/ρ)e-e1)-T(((ρ1)/ρ)s-s1))/(((ρ1)/ρ)p) ratio"}(*,MaxPlotPoints->60*)]
ListPlot[Table[{Ratios4κ[[j,1]],((((ρ2)/ρ)(e1+e2)-e2)-T(((ρ2)/ρ)s-s2))/(((ρ2)/ρ) p)/.m1->m2/Ratios4κ[[j,1]]/.ρ1->Ratios4κ[[j,2]]/.ρ2->Ratios4κ[[j,3]]/.u1->Ratios4κ[[j,4]]/.u2->Ratios4κ[[j,5]]/.e1->Ratios4κ[[j,6]]/.e2->Ratios4κ[[j,7]]/.p->Ratios4κ[[j,8]] },{j,1,κnum+1}],AxesLabel->{"κ","((((ρ2)/ρ)e-e2)-T(((ρ2)/ρ)s-s2))/(((ρ2)/ρ)p) ratio"}(*,MaxPlotPoints->60*)]
ListPlot[Table[{Ratios4κ[[j,1]],(p1-((ρ1/m1)/(ρ1/m1+ρ2/m2))p)/(((ρ1/m1)/(ρ1/m1+ρ2/m2)) p)/.m1->m2/Ratios4κ[[j,1]]/.ρ1->Ratios4κ[[j,2]]/.ρ2->Ratios4κ[[j,3]]/.u1->Ratios4κ[[j,4]]/.u2->Ratios4κ[[j,5]]/.e1->Ratios4κ[[j,6]]/.e2->Ratios4κ[[j,7]]/.p->Ratios4κ[[j,8]]/.p1->Ratios4κ[[j,9]]/.p2->Ratios4κ[[j,10]]},{j,1,κnum+1}],AxesLabel->{"κ","\!\(TraditionalForm\`\((\*SubscriptBox[\(p\), \(1\)] - \*SubscriptBox[\(x\), \(1\)]\\ p)\)/\((\*SubscriptBox[\(x\), \(1\)] p)\)\)"}(*,MaxPlotPoints->60*)]
ListPlot[Table[{Ratios4κ[[j,1]],(p2-((ρ2/m2)/(ρ1/m1+ρ2/m2))p)/(((ρ2/m2)/(ρ1/m1+ρ2/m2)) p)/.m1->m2/Ratios4κ[[j,1]]/.ρ1->Ratios4κ[[j,2]]/.ρ2->Ratios4κ[[j,3]]/.u1->Ratios4κ[[j,4]]/.u2->Ratios4κ[[j,5]]/.e1->Ratios4κ[[j,6]]/.e2->Ratios4κ[[j,7]]/.p->Ratios4κ[[j,8]]/.p1->Ratios4κ[[j,9]]/.p2->Ratios4κ[[j,10]]},{j,1,κnum+1}],AxesLabel->{"κ","\!\(TraditionalForm\`\((\*SubscriptBox[\(p\), \(2\)] - \*SubscriptBox[\(x\), \(2\)]\\ p)\)/\((\*SubscriptBox[\(x\), \(2\)] p)\)\)"}(*,MaxPlotPoints->60*)]

matches the explicit results

Without the explicit expressions - vdW gas

s1=(3/2)(kB/m1) ρ1 Log[(T1/Tref)]-(kB/m1) ρ1 Log[C1 ((ρ1/m1)/(1-ν1 ρ1/m1))]/.T1->(e1-(1/2)((u1^2)/(ρ1))-a1 ((ρ1)^2))((((3/2)(kB/m1)ρ1))^(-1));
s2=(3/2)(kB/m2) ρ2 Log[(T2/Tref)]-(kB/m2) ρ2 Log[C2 ((ρ2/m2)/(1-ν2 ρ2/m2))]/.T2->(e2-(1/2)((u2^2)/(ρ2))-a2 ((ρ2)^2))((((3/2)(kB/m2)ρ2))^(-1));
s=s1+s2;

FirstMEstep={D[s,ρ1]==ρstar,D[s,ρ2]==ρstar,D[s,u1]==ustar,D[s,u2]==ustar,D[s,e1]==estar,D[s,e2]==estar}//Simplify;

instead of the second step, we use projections

Projections={ρ==ρ1+ρ2,u==u1+u2,e==e1+e2};

(*free ene fE=e-Ts; pressure p=ρ (∂_ρ)fE-fE*)
fE=(3/2)(kB/m)ρ T+(1/2)((u^2)/ρ)-a (ρ^2)-T ((3/2)(kB/m) ρ Log[(T/Tref)]-(kB/m) ρ Log[C ((ρ/m)/(1-ν ρ/m))])//Simplify
ρ D[fE,ρ]-fE//Simplify

%/.u->0//Simplify

kB=1.380649 (10^(-23));(*J/K*)
h=6.62607015 (10^(-34)); (*J/Hz*)
Da=1.66053906660 (10^(-27));(*kg*)

κnum=100;κmin=0.1;κmax=5;Ratios4κ=Table[{},{i,1,κnum+1}];Clear[j,p,p1,p2,e,T,estar,κ,m1,m2];
For[j=1,j≤κnum+1,j++,
κ=κmin+(j-1) (κmax-κmin)/κnum;
m2=10 Da;(*mol mass*)
m1=m2/κ; (*κ=m2/m1*) 
Tref=300; (*K*)
C1=(1/10)(m1/ρ);
C2=(1/10)(m2/ρ);
a1=3 (10^(-49))/(m1^2);
a2=3 (10^(-49))/(m2^2);
ν1=(10^(-28));
ν2=0.5 (10^(-28));
(*mixture state variables*)
ρ=1; (*kg/(m^3)*)
u=0 (10^3); (*kg m/s*) (*and hence total and interal energies are equal*)
T=300;
estar=1/T;
eestimate=(3/2)kB/estar((ρ/((m1+m2)/2)))+(1/2)((u^2)/ρ);
numEstimate=Chop[FindRoot[FirstMEstep⋃Projections,{{ρ1,ρ(0.8-(0.6/4)κ)},{ρ2,ρ(1-(0.8-(0.6/4)κ))},{u1,u/2},{u2,u/2},{e1,eestimate/2},{e2,eestimate/2},{ρstar,(10^3)},{ustar,1},{e,eestimate}}]];
p=(-e+ρ μ+T s)/.μ->(-ρstar T)/.numEstimate;
p1=-e1+ρ1 μ+T s1/.μ->(-ρstar T)/.numEstimate;
p2=-e2+ρ2 μ+T s2/.μ->(-ρstar T)/.numEstimate;
Ratios4κ[[j]]={κ,ρ1/.numEstimate,ρ2/.numEstimate,u1/.numEstimate,u2/.numEstimate,e1/.numEstimate,e2/.numEstimate,p,p1,p2}];

Clear[j,p,p1,p2,m1,κ,estar]

ListPlot[{Table[{Ratios4κ[[j,1]],((((ρ1)/ρ)(e1+e2)-e1)-T(((ρ1)/ρ)s-s1))/(((ρ1)/ρ) p)/.m1->m2/Ratios4κ[[j,1]]/.ρ1->Ratios4κ[[j,2]]/.ρ2->Ratios4κ[[j,3]]/.u1->Ratios4κ[[j,4]]/.u2->Ratios4κ[[j,5]]/.e1->Ratios4κ[[j,6]]/.e2->Ratios4κ[[j,7]]/.p->Ratios4κ[[j,8]] },{j,1,κnum+1}],Table[{Ratios4κ[[j,1]],((((ρ2)/ρ)(e1+e2)-e2)-T(((ρ2)/ρ)s-s2))/(((ρ2)/ρ) p)/.m1->m2/Ratios4κ[[j,1]]/.ρ1->Ratios4κ[[j,2]]/.ρ2->Ratios4κ[[j,3]]/.u1->Ratios4κ[[j,4]]/.u2->Ratios4κ[[j,5]]/.e1->Ratios4κ[[j,6]]/.e2->Ratios4κ[[j,7]]/.p->Ratios4κ[[j,8]] },{j,1,κnum+1}]},AxesStyle -> Thickness[0.0025],PlotTheme->{"Monochrome"},LabelStyle->{FontSize->16,Black},AxesLabel -> {Style["κ"(*"\kappa"*), FontFamily->"Times",FontSize -> 20]}]

ListPlot[{Table[{Ratios4κ[[j,1]],100 (p1-((ρ1/m1)/(ρ1/m1+ρ2/m2))p)/(((ρ1/m1)/(ρ1/m1+ρ2/m2)) p)/.m1->m2/Ratios4κ[[j,1]]/.ρ1->Ratios4κ[[j,2]]/.ρ2->Ratios4κ[[j,3]]/.u1->Ratios4κ[[j,4]]/.u2->Ratios4κ[[j,5]]/.e1->Ratios4κ[[j,6]]/.e2->Ratios4κ[[j,7]]/.p->Ratios4κ[[j,8]]/.p1->Ratios4κ[[j,9]]/.p2->Ratios4κ[[j,10]]},{j,1,κnum+1}],Table[{Ratios4κ[[j,1]],100 (p2-((ρ2/m2)/(ρ1/m1+ρ2/m2))p)/(((ρ2/m2)/(ρ1/m1+ρ2/m2)) p)/.m1->m2/Ratios4κ[[j,1]]/.ρ1->Ratios4κ[[j,2]]/.ρ2->Ratios4κ[[j,3]]/.u1->Ratios4κ[[j,4]]/.u2->Ratios4κ[[j,5]]/.e1->Ratios4κ[[j,6]]/.e2->Ratios4κ[[j,7]]/.p->Ratios4κ[[j,8]]/.p1->Ratios4κ[[j,9]]/.p2->Ratios4κ[[j,10]]},{j,1,κnum+1}]},AxesStyle -> Thickness[0.0025],PlotTheme->{"Monochrome"},LabelStyle->{FontSize->16,Black},AxesLabel -> {Style["κ"(*"\kappa"*), FontFamily->"Times",FontSize -> 20]}]