how can I solve non polynomial equations.

R=0.082

a=4.225

b=0.037

T=320

eqn1 : P+(a/v1^2) - RT/(v1-b)=0

eqn2 : P+(a/v2^2) - RT/(v2-b)=0

eqn3 : P(v1-v2)-RTln(v1-b/v2-b)-a(1/v1 -1/v2)=0

Answer 1

[Star Strider]

FIRST: see Getting Started. What you posted is not valid MATLAB code.

There may be many solutions, depending on the initial estimates:

R = 0.082;
a = 4.225;
b = 0.037;
T = 320;
eqn1 = @(v1,v2,P) P+(a./v1^2) - R*T/(v1-b);
eqn2 = @(v1,v2,P) P+(a./v2^2) - R*T/(v2-b);
eqn3 = @(v1,v2,P) P*(v1-v2)-R*T*log(v1-b./v2-b)-a*(1./v1 -1./v2);

[Vv,fval] = fsolve(@(b) [eqn1(b(1),b(2),b(3)); eqn2(b(1),b(2),b(3)); eqn3(b(1),b(2),b(3))], ones(3,1))

producing:

Vv =
   1.071530062473936
   1.071530062474078
  21.684426220811453


fval =
   1.0e-11 *
  -0.252597942562716
  -0.001776356839400
  -0.189449129302390

Experiment to get the result you want.

[Dongmin Kim]

then, what are the b(1), b(2), b(3)?

[Star Strider]

They are: ‘v1’, ‘v2’, and ‘P’, respectively.

[Dongmin Kim]

thanks!

[Star Strider]

As always, my pleasure!