Nonlinear Equation Solution
| Variable | Value | f(x) | Initial value | Initial f(x) | |
|---|---|---|---|---|---|
| 1 | V | 0.57489191 | 5.9e-11 | 0.9958 | 2.1e+1 |
| 2 | P | 56 | 56 | ||
| 3 | R | 0.08206 | 0.08206 | ||
| 4 | T | 450 | 450 | ||
| 5 | Tc | 405.5 | 405.5 | ||
| 6 | Pc | 111.3 | 111.3 | ||
| 7 | Pr | 0.50314465 | 0.5031 | ||
| 8 | a | 4.1969459 | 4.197 | ||
| 9 | b | 0.037371215 | 0.03737 | ||
| 10 | Z | 0.87182677 | 1.51 |
Root Finding Plot
Settings and Hints
| Name/Source | Value | Type | |
|---|---|---|---|
| 1 | Number of equations | 10 | Setting |
| 2 | Implicit equations | 1 | Setting |
| 3 | Explicit equations | 9 | Setting |
| 4 | Elapsed time | 0.000 ms | Setting |
| 5 | Solution method | Brent | Setting |
| 6 | Tolerance F | 1e-7 | Setting |
| 7 | Max iterations | 150 | Setting |
| 8 | #@chart_size = 428,300 | Default (array) | |
| 9 | #@report_fix_digits = 8 | Default (integer) | |
| 10 | #@report_show_source = true | Default (boolean) | |
| 11 | #@report_show_header = false | Default (boolean) | |
| 12 | #@report_show_charts = true | Default (boolean) | |
| 13 | #@report_show_settings = true | Default (boolean) | |
Messages
| Severity | Description | |
|---|---|---|
| 1 | Info | -Infor- Implicit variables (1) V |
| 2 | Info | -Infor- Explicit variables (9) P, R, T, Tc, Pc, Pr, a, b, Z |
| 3 | Info | -Infor- All variables (10) P, a, V, b, R, T, Tc, Pc, Pr, Z |
Source
# 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
# 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