Solving a system of 7 equations with solve is producing empty solutions, any ideas?

Here is what I had. The issue is that it won't find the solution for each LoLo A1 L1 gp1 gp2 g1 g2 but rather returns an empty response for each. No errors came up- the solution sol is just empty.

R=8.314; %gas constant (J/(Kmol))
T=1573.15; %isothermal hold T (K)

A2=(1-2*0.925)-(1-2*0.16);
A3=(6*0.925^2-6*0.925+1)-(6*0.16^2-6*0.16+1);

syms Lo A1 L1 gp1 gp2 g1 g2 ; 
equ1=(g1-gp1*0.16)-(g2-gp2*0.925);
equ2=R*T*(log(0.16)-log(1-0.16))-R*T*(log(0.925)-log(1-0.925))-A1; 
equ3=(A2*Lo-A1)/A3-L1; equ4=R*T*(log(0.16)-log(1-0.16))+Lo*(1-2*0.16)-L1*(6*0.16^2-6*0.16+1)-gp1; 
equ5=R*T*(log(0.925)-log(1-0.925))+Lo*(1-2*0.925)-L1*(6*0.925^2-6*0.925+1)-gp2;
equ6=0.16*(1-0.16)*(Lo+L1*(2*0.16-1))+R*T*(0.16*log(0.16)+(1-0.16)*log(1-0.16))-g1; 
equ7=0.925*(1-0.925)*(Lo+L1*(2*0.925-1))+R*T*(0.925*log(0.925)+(1-0.925)*log(1-0.925))-g2; 
sol=solve(equ1,equ2,equ3,equ4,equ5,equ6,equ7);

Answer 1

[Walter Roberson]

It is capable of solution, at least if you switch to rational values. The solution set is

g2 = (343589772257/5618160000) * ln(4/25) + (2143806607181/1872720000) * ln(21/25) + (21133190640089/1755675000) * ln(37/40) - (95870309503/585225000) * ln(3/40)

g1 = -(919857962803/877837500) * ln(4/25) + (12238047735179/1170450000) * ln(21/25) + (3446099474468/1097296875) * ln(37/40) + (194094869444/365765625) * ln(3/40)

gp2 = (150541236341/33379500) * ln(4/25) - (3258413397883/76296000) * ln(21/25) + (14648669392/5960625) * ln(37/40) - (14648669392/5960625) * ln(3/40) + (45875/15708) * g1

gp1 = gp2

Lo = -(61079719697/4492080) * ln(4/25) + (61079719697/4492080) * ln(21/25) + (31651589222/7018875) * ln(37/40) - (31651589222/7018875) * ln(3/40) + (255/367) * gp1

L1 = -(200/51) * Lo - (261583382/7803) * ln(4/25) + (261583382/7803) * ln(21/25) + (261583382/7803) * ln(37/40) - (261583382/7803) * ln(3/40)

A1 = (130791691/10000) * ln(4/25) - (130791691/10000) * ln(21/25) - (130791691/10000) * ln(37/40) + (130791691/10000) * ln(3/40)

[Alyssa]

I forgot to say Thank you Walter! :)

Answer 2

[Roger Stafford]

Those equations are all linear in the seven unknowns, and there is no reason 'solve' shouldn't be able to solve them very easily. You could actually have used matrix division for solving them.

Have you tried specifying the unknowns in your call to 'solve'? That may be the trouble - 'solve' doesn't know which are the unknowns to solve for.

[Alyssa]

Hi Roger - Yes I had tried it with specification for the unknowns in solve. But thank you! :)