Numeric solution for a set of equations

What's up, guys? I'm new to Matlab, so I apologize for my lack of knowledge. I've been trying to solve a set of 4 equations from a thermodynamics problem but I can't seem to get Matlab to work properly.

The equations are :

0.70*P = 0.35 * Psat1;

0.30*P = 0.65 * Psat2;

log (Psat1) = 13.7819 - 2726.81/(t + 217.572);

log (Psat2) = 13.9726 -3259.93/(t + 212.300);

I want to solve them for P and t (eq. 1 and 2 could eventually go into 3 and 4 thus making a 2 variable system but I chose to write the 4 eqs. anyway). I used the vpasolve function, with eq1 - eq4 being those above, but I got this:

>> syms P t Psat1 Psat2
>> vpasolve([eq1, eq2, eq3, eq4], [P t Psat1 Psat2])

ans = 

          P: [1x1 sym]
          t: [1x1 sym]
      Psat1: [1x1 sym]
      Psat2: [1x1 sym]

What am I doing wrong? Is there a better function to solve this kind of problem?

Answer 1

[Star Strider]

Try this:

syms P t Psat1 Psat2
eq1 = 0.70*P == 0.35 * Psat1;
eq2 = 0.30*P == 0.65 * Psat2;
eq3 = log(Psat1) == 13.7819 - 2726.81/(t + 217.572);
eq4 = log(Psat2) == 13.9726 -3259.93/(t + 212.300);
[P, t, Psat1, Psat2] = vpasolve([eq1, eq2, eq3, eq4], [P t Psat1 Psat2])

P =
207.45534890683278690964114324486

t =
134.10035388099313659241316466853

Psat1 =
414.91069781366557381928228648973

Psat2 =
95.748622572384363189065143036091

EDIT — Added output.

[Walter Roberson]

Caution: there is a second solution with negative t and the other values on the order of 10^53 . vpasolve() might find either of them unless you add a restriction to the range. For example,

syms P t Psat1 Psat2 positive

[Star Strider]

@Walter — Excellent point. When the solutions I got seemed reasonable, I didn’t explore the complete solution space.