# Example 7 - Single NLE
# Molar Volume: Van Der Waals equation.
# Verified Solution: V=0.574892, Z=0.871827
# Ref.: Comput. Appl. Eng. Educ. 6: 171-172, 1998
f(V)=(P+a/(V^2))*(V-b)-R*T
P=56
R=0.08206
T=450
Tc=405.5
Pc=111.3
Pr=P/Pc
a=27*(R^2*Tc^2/Pc)/64
b=R*Tc/(8*Pc)
Z=P*V/(R*T)
V(min)=0.4
V(max)=1
Calculated values
| |
Variable |
Value |
f(x) |
Initial Guess |
Initial f(x) |
| 1 |
V |
0.57489191 |
3.2E-10 |
0.7 |
5.9E00 |
| |
Variable |
Value |
Initial Value |
| 1 |
a |
4.1969459 |
4.1969459 |
| 2 |
b |
0.03737122 |
0.03737122 |
| 3 |
P |
56 |
56 |
| 4 |
Pc |
111.3 |
111.3 |
| 5 |
Pr |
0.50314465 |
0.50314465 |
| 6 |
R |
0.08206 |
0.08206 |
| 7 |
T |
450 |
450 |
| 8 |
Tc |
405.5 |
405.5 |
| 9 |
Z |
0.87182677 |
1.0615539 |
Root Finding Plot

Formatted equations
Nonlinear equations
| 1 |
f(V) = (P+a/(V^2))*(V-b)-R*T = 0 |
Explicit equations
| 1 |
P = 56 |
| 2 |
R = 0.08206 |
| 3 |
T = 450 |
| 4 |
Tc = 405.5 |
| 5 |
Pc = 111.3 |
| 6 |
Pr = P/Pc |
| 7 |
a = 27*(R^2*Tc^2/Pc)/64 |
| 8 |
b = R*Tc/(8*Pc) |
| 9 |
Z = P*V/(R*T) |
General Settings
| Total number of equations |
10 |
| Number of implicit equations |
1 |
| Number of explicit equations |
9 |
| Elapsed time |
0.00 sec |
| Reporting digits |
10 |
| Solution method |
safenewt |
| Max iterations |
150 |
| Tolerance F |
1E-07 |
| Tolerance X |
1E-07 |
| Tolerance min |
1E-07 |