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IAPWS IF97 Verification Tables
The baseline tables below are printed for verification purposes. Developers should compare the output from the top-level IF97.cpp program in this repository to these baseline results for any regressions. Unless otherwise noted, tables below are reproduced from the "Revised Release on the IAPWS Industrial Formulation 1997" IAPWS R7-97(2012). The tables below are broken up into three sections,
(Regions 1, 2, 3, 5 - 3 pts. each)
| T | p | v | h | u | s | cp | w |
|---|---|---|---|---|---|---|---|
| [K] | [MPa] | [m³/kg] | [kJ/kg] | [kJ/kg] | [kJ/kg-K] | [kJ/kg-K] | [m/s] |
| 300 | 3 | 1.00215168e-03 | 1.15331273e+02 | 1.12324818e+02 | 3.92294792e-01 | 4.17301218e+00 | 1.50773921e+03 |
| 300 | 80 | 9.71180894e-04 | 1.84142828e+02 | 1.06448356e+02 | 3.68563852e-01 | 4.01008987e+00 | 1.63469054e+03 |
| 500 | 3 | 1.20241800e-03 | 9.75542239e+02 | 9.71934985e+02 | 2.58041912e+00 | 4.65580682e+00 | 1.24071337e+03 |
| 300 | 0.0035 | 3.94913866e+01 | 2.54991145e+03 | 2.41169160e+03 | 8.52238967e+00 | 1.91300162e+00 | 4.27920172e+02 |
| 700 | 0.0035 | 9.23015898e+01 | 3.33568375e+03 | 3.01262819e+03 | 1.01749996e+01 | 2.08141274e+00 | 6.44289068e+02 |
| 700 | 30 | 5.42946619e-03 | 2.63149474e+03 | 2.46861076e+03 | 5.17540298e+00 | 1.03505092e+01 | 4.80386523e+02 |
| 650 | 25.5837 | 0.002 | 1.86343019e+03 | 1.81226279e+03 | 4.05427273e+00 | 1.38935718e+01 | 5.02005553e+02 |
| 650 | 22.29306 | 0.005 | 2.37512400e+03 | 2.26365868e+03 | 4.85438790e+00 | 4.46579373e+01 | 3.83444592e+02 |
| 750 | 78.30956 | 0.002 | 2.25868845e+03 | 2.10206932e+03 | 4.46971906e+00 | 6.34165360e+00 | 7.60696041e+02 |
| 1500 | 0.5 | 1.38455090e+00 | 5.21976855e+03 | 4.52749310e+03 | 9.65408875e+00 | 2.61609445e+00 | 9.17068690e+02 |
| 1500 | 30 | 2.30761299e-02 | 5.16723514e+03 | 4.47495124e+03 | 7.72970133e+00 | 2.72724317e+00 | 9.28548002e+02 |
| 2000 | 30 | 3.11385219e-02 | 6.57122604e+03 | 5.63707038e+03 | 8.53640523e+00 | 2.88569882e+00 | 1.06736948e+03 |
________________________________________________ RELATIVE ERROR ___________________________________________
| T | p | v | h | u | s | cp | w |
|---|---|---|---|---|---|---|---|
| [K] | [MPa] | [rel. err.] | [rel. err.] | [rel. err.] | [rel. err.] | [rel. err.] | [rel. err.] |
| 300 | 3 | 3.1263e-10 | 1.8589e-10 | 1.5688e-10 | 1.0263e-09 | 9.7478e-10 | 2.1951e-10 |
| 300 | 80 | 2.2272e-11 | 1.4431e-09 | 1.9965e-09 | 1.0812e-09 | 8.8195e-11 | 1.9035e-09 |
| 500 | 3 | 2.8096e-09 | 9.9663e-11 | 8.9605e-11 | 2.0078e-11 | 4.5346e-10 | 2.5000e-09 |
| 300 | 0.0035 | 9.5623e-10 | 3.2943e-10 | 9.9190e-10 | 3.1261e-10 | 5.1408e-10 | 6.1485e-10 |
| 700 | 0.0035 | 1.8873e-10 | 1.1186e-09 | 2.0904e-10 | 2.1036e-09 | 1.7788e-09 | 6.7277e-10 |
| 700 | 30 | 8.5049e-10 | 1.8411e-09 | 4.0254e-10 | 4.4423e-10 | 7.9528e-10 | 3.5333e-10 |
| 650 | 25.5837 | 5.9835e-10 | 9.5784e-11 | 1.9062e-09 | 9.6775e-10 | 6.3495e-09 | 1.7489e-09 |
| 650 | 22.29306 | 1.6306e-08 | 5.8939e-09 | 1.6263e-09 | 3.1159e-09 | 6.8982e-08 | 6.0169e-09 |
| 750 | 78.30956 | 1.3706e-10 | 1.9751e-09 | 1.0858e-09 | 8.1286e-10 | 9.1506e-10 | 3.2359e-10 |
| 1500 | 0.5 | 8.8005e-10 | 2.3149e-10 | 4.0145e-10 | 3.4317e-10 | 1.5075e-09 | 3.2919e-10 |
| 1500 | 30 | 2.0477e-09 | 1.7324e-11 | 3.7361e-10 | 4.9384e-10 | 8.3254e-10 | 2.2699e-10 |
| 2000 | 30 | 9.6709e-10 | 2.1024e-10 | 4.4738e-10 | 1.3332e-10 | 4.2249e-10 | 1.1454e-09 |
Note
Relative errors above should be on the order of 1E-8 or lower.
The RMS all relative errors (72) is 8.514e-09
Note
The values of v in region 3 in the above table (rows 6-8) are evaluated first using the supplemental backward equations for v(T,p) from IAPWS SR5-05(2016). These values are then used as the initial values to iterate on the p(T,v) equation from IAPWS R7-97(2012). IAPWS explains that the values from v(T,p) could be used directly, but that they may be up to 1E-6 in error. By iterating on p(T,v) using the v(T,p) values as initial estimates, the relative error is reduced to the order of 1E-8 and computation time is greatly reduced.
(Region 3 direct formulation for v(T,p))
| T | p | v (iter.) | error* | v (direct) | error |
|---|---|---|---|---|---|
| [K] | [ MPa ] | [ m³/kg ] | [ -rel.- ] | [ m³/kg ] | [ -rel.- ] |
| 670 | 80 | 1.50382884e-03 | 1.6767e-06 | 1.50383136E-03 | 3.0557E-10 |
| 710 | 50 | 2.20473856e-03 | 4.5235e-06 | 2.20472859E-03 | 2.6073E-11 |
| 750 | 80 | 1.97369363e-03 | 3.5107e-07 | 1.97369294E-03 | 6.1365E-11 |
| 630 | 20 | 1.76169156e-03 | 2.7517e-06 | 1.76169641E-03 | 2.6706E-10 |
| 650 | 30 | 1.81956936e-03 | 4.8036e-06 | 1.81956062E-03 | 2.5895E-10 |
| 656 | 26 | 2.24558013e-03 | 3.3797e-06 | 2.24558772E-03 | 1.3273E-11 |
| 670 | 30 | 2.50689561e-03 | 8.3575e-07 | 2.50689770E-03 | 1.4776E-10 |
| 661 | 26 | 2.97023430e-03 | 2.8068e-06 | 2.97022596E-03 | 1.0597E-12 |
| 675 | 30 | 3.00464378e-03 | 5.5556e-06 | 3.00462709E-03 | 1.1915E-10 |
| 671 | 26 | 5.01903333e-03 | 7.8208e-07 | 5.01902940E-03 | 8.9081E-12 |
| 690 | 30 | 4.65645893e-03 | 2.4083e-06 | 4.65647014E-03 | 6.7512E-11 |
| 649 | 23.6 | 2.16319583e-03 | 1.1800e-06 | 2.16319838E-03 | 1.4503E-10 |
| 650 | 24 | 2.16604799e-03 | 1.7690e-06 | 2.16604416E-03 | 2.0090E-11 |
| 652 | 23.6 | 2.65109229e-03 | 4.1045e-06 | 2.65108141E-03 | 1.6074E-10 |
| 654 | 24 | 2.96779551e-03 | 2.3003e-06 | 2.96780233E-03 | 2.0292E-11 |
| 653 | 23.6 | 3.27392646e-03 | 2.9467e-06 | 3.27391682E-03 | 1.9591E-11 |
| 655 | 24 | 3.55033843e-03 | 2.4136e-06 | 3.55032986E-03 | 9.5912E-11 |
| 655 | 23.5 | 4.54499387e-03 | 1.6002e-06 | 4.54500114E-03 | 7.7144E-11 |
| 660 | 24 | 5.10028320e-03 | 3.0384e-06 | 5.10026770E-03 | 8.3681E-11 |
| 660 | 23 | 6.10953778e-03 | 1.9288e-06 | 6.10952600E-03 | 1.8546E-11 |
| 670 | 24 | 6.42733198e-03 | 9.8553e-07 | 6.42732564E-03 | 4.6431E-11 |
| 646 | 22.6 | 2.11786544e-03 | 2.1646e-06 | 2.11786085E-03 | 1.5199E-10 |
| 646 | 23 | 2.06237253e-03 | 1.0413e-06 | 2.06237467E-03 | 7.1144E-11 |
| 648.6 | 22.6 | 2.53305902e-03 | 1.8774e-06 | 2.53306378E-03 | 1.6639E-10 |
| 649.3 | 22.8 | 2.57297103e-03 | 2.9184e-07 | 2.57297178E-03 | 3.3022E-11 |
| 649 | 22.6 | 2.92343611e-03 | 1.1630e-06 | 2.92343271E-03 | 6.0169E-13 |
| 649.7 | 22.8 | 2.91330884e-03 | 9.1270e-07 | 2.91331149E-03 | 1.4168E-11 |
| 649.1 | 22.6 | 3.13121119e-03 | 7.0122e-07 | 3.13120900E-03 | 2.0784E-12 |
| 649.9 | 22.8 | 3.22116335e-03 | 9.5350e-07 | 3.22116028E-03 | 1.9780E-11 |
| 649.4 | 22.6 | 3.71558408e-03 | 3.2581e-06 | 3.71559619E-03 | 1.3115E-10 |
| 650.2 | 22.8 | 3.66476716e-03 | 3.3745e-06 | 3.66475479E-03 | 1.0404E-10 |
| 640 | 21.1 | 1.97099683e-03 | 1.2374e-06 | 1.97099927E-03 | 5.4816E-11 |
| 643 | 21.8 | 2.04391649e-03 | 1.3082e-06 | 2.04391916E-03 | 4.2142E-11 |
| 644 | 21.1 | 5.25100574e-03 | 7.9556e-07 | 5.25100992E-03 | 1.9107E-11 |
| 648 | 21.8 | 5.25684493e-03 | 3.5937e-08 | 5.25684474E-03 | 4.1829E-11 |
| 635 | 19.1 | 1.93282776e-03 | 6.8398e-07 | 1.93282908E-03 | 1.3642E-11 |
| 638 | 20 | 1.98539065e-03 | 1.7237e-06 | 1.98538723E-03 | 2.3807E-10 |
| 626 | 17 | 8.48333686e-03 | 8.8241e-06 | 8.48326200E-03 | 1.6488E-11 |
| 640 | 20 | 6.22750753e-03 | 3.3036e-06 | 6.22752810E-03 | 1.1142E-12 |
| 644.6 | 21.5 | 2.26690985e-03 | 6.4222e-04 | 2.26836665E-03 | 1.6335E-10 |
| 646.1 | 22 | 2.29627896e-03 | 3.1177e-05 | 2.29635055E-03 | 1.1112E-10 |
| 648.6 | 22.5 | 2.83221289e-03 | 5.6621e-05 | 2.83237326E-03 | 8.8933E-11 |
| 647.9 | 22.3 | 2.81156973e-03 | 5.1689e-05 | 2.81142440E-03 | 1.5763E-10 |
| 647.5 | 22.15 | 3.69403449e-03 | 5.9776e-07 | 3.69403228E-03 | 1.0865E-10 |
| 648.1 | 22.3 | 3.62139136e-03 | 2.3051e-04 | 3.62222631E-03 | 1.1009E-10 |
| 648 | 22.11 | 4.52465980e-03 | 7.5371e-04 | 4.52807265E-03 | 3.7006E-11 |
| 649 | 22.3 | 4.55814914e-03 | 2.7285e-04 | 4.55690580E-03 | 2.6973E-11 |
| 646.84 | 22 | 2.68226364e-03 | 5.9633e-03 | 2.69835472E-03 | 2.7941E-11 |
| 647.05 | 22.064 | 2.67687478e-03 | 1.5006e-02 | 2.71765565E-03 | 5.6638E-11 |
| 646.89 | 22 | 3.77879512e-03 | 5.2486e-03 | 3.79873296E-03 | 3.3706E-11 |
| 647.15 | 22.064 | 3.73521982e-03 | 8.9898e-03 | 3.70194001E-03 | 2.2565E-10 |
Note
* Error values above should be on the order of 1E-6 or lower, except the last dozen, which are very near
the critical point and can be as high as 1.5E-2. However, since the calculated values are actually
using the IF97 iterative solution in region 3, the error is actually the distance from these initial guess
values to the more accurate iterative solution, not the actual error in the formulation. See next NOTE below.
To see the actual error in this explicit equation, undefine the REGION3_ITERATE flag at the top of this
file to turn off the iterative solution and provide just the explicit results from v(p,T). Doing so will
increase the error in the previous verification table to the order of 1E-6 for points in region 3, but
drop the relative error in this table (shown in the second column of values) to on the order of 1E-10.
Note
IAPWS-IF97 is covered by a basic equation for the Helmholtz free energy, f(v,T). In some steam power cycles, thermodynamic properties as a function of (p,T) are required in region 3. This requires iteration of the Helmhotz equation to find v from p and T. To avoid this iterative solution, IAPWS has provided a supplementary release with explicit equations for v as a function of T and P in region 3, dramatically speeding up these calculations. The RMS Error with REGION3_ITERATE turned off should be 1.132e-10 or less.
| Table 35 | Table 36 |
|---|---|
| ________ Saturation Pressures _________ | ______ Saturation Temperatures ________ |
| T/K | p/MPa | err | p/MPa | T/K | err |
|---|---|---|---|---|---|
| 300 | 3.536589413e-03 | 8.5e-08 | 0.1 | 3.72755919e+02 | -1.0e-07 |
| 500 | 2.638897756e+00 | -1.4e-07 | 1.0 | 4.53035632e+02 | 8.6e-08 |
| 600 | 1.234431458e+01 | -1.8e-07 | 10.0 | 5.84149488e+02 | -2.5e-10 |
| Speed Test |
|---|
| Timing (100k Tsat calls): 0.7607 ms |
| Timing (100k psat calls): 0.4523 ms |
These reverse functions take inputs of pressure and enthalpy (p, h), pressure and entropy (p, s), or enthalpy and entropy (h, s) to define the state point. These functions are commonly used in evaluating constant enthalpy or entropy steps in energy cycles (e.g. through expansions, compressors, turbines, etc.).
The verification table below contain contains the published T(p,h) and T(p,s) values for verification of computer programs from Table 7 (p. 11) and Table 24 (p. 25) of IAPWS R7-97(2012), as well as Table 5 (p. 8) of Reference IAPWS SR3-03(2014).
| Region | p | h | T | error | : | p | s/(kJ/kg/K) | T/K | error |
|---|---|---|---|---|---|---|---|---|---|
| [MPa] | [kJ/kg] | [K] | [relative] | [MPa] | [kJ/kg/K] | [K] | [relative] | ||
| 1 | 3 | 500 | 3.91798509e+02 | 6.064e-10 | 3 | 0.5 | 3.07842258e+02 | 1.166e-09 | |
| 1 | 80 | 500 | 3.78108626e+02 | 3.190e-10 | 80 | 0.5 | 3.09979785e+02 | 5.853e-10 | |
| 1 | 80 | 1500 | 6.11041229e+02 | 6.590e-10 | 80 | 3 | 5.65899909e+02 | 4.268e-10 | |
| 2a | 0.001 | 3000 | 5.34433241e+02 | 7.143e-10 | 0.1 | 7.5 | 3.99517097e+02 | 8.625e-10 | |
| 2a | 3 | 3000 | 5.75373370e+02 | 4.145e-10 | 0.1 | 8 | 5.14127081e+02 | 8.677e-10 | |
| 2a | 3 | 4000 | 1.01077577e+03 | 4.293e-09 | 2.5 | 8 | 1.03984917e+03 | 3.111e-09 | |
| 2b | 5 | 3500 | 8.01299102e+02 | 1.795e-10 | 8 | 6 | 6.00484040e+02 | 3.113e-10 | |
| 2b | 5 | 4000 | 1.01531583e+03 | 4.603e-09 | 8 | 7.5 | 1.06495556e+03 | 4.025e-09 | |
| 2b | 25 | 3500 | 8.75279054e+02 | 3.182e-10 | 90 | 6 | 1.03801126e+03 | 7.771e-10 | |
| 2c | 40 | 2700 | 7.43056411e+02 | 5.099e-11 | 20 | 5.8 | 6.97992849e+02 | 6.646e-10 | |
| 2c | 60 | 2700 | 7.91137067e+02 | 5.912e-10 | 80 | 5.2 | 8.54011484e+02 | 4.698e-11 | |
| 2c | 60 | 3200 | 8.82756860e+02 | 3.973e-10 | 80 | 5.8 | 9.49017998e+02 | 4.526e-10 | |
| 3a | 20 | 1700 | 6.29308389e+02 | 6.454e-11 | 20 | 3.8 | 6.28295987e+02 | 4.859e-11 | |
| 3a | 50 | 2000 | 6.90571834e+02 | 1.838e-11 | 50 | 3.6 | 6.29715873e+02 | 4.475e-11 | |
| 3a | 100 | 2100 | 7.33616301e+02 | 6.215e-11 | 100 | 4 | 7.05688024e+02 | 5.885e-11 | |
| 3b | 20 | 2500 | 6.41841805e+02 | 3.622e-11 | 20 | 5 | 6.40117644e+02 | 5.590e-11 | |
| 3b | 50 | 2400 | 7.35184862e+02 | 1.057e-11 | 50 | 4.5 | 7.16368752e+02 | 3.735e-11 | |
| 3b | 100 | 2700 | 8.42046088e+02 | 3.950e-11 | 100 | 5 | 8.47433282e+02 | 4.080e-11 |
Note
Relative errors above should be on the order of 1E-9 or lower.
The RMS of all relative errors (36) is 1.419e-09
Note
The Region 3a, 3b validation comes from Table 5 & 12 of the 2014 "Revised Supplementary Release on Backward Equations for the functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3" IAPWS SR3-03(2014)"
Note
While IAPWS SR3-03(2014) provides direct reverse functions for v(p,h) and v(p,s) in region 3, these are not used in this implementation because [IAPWS R7-97(2012)] does not provide them for regions 1, 2, and 5. Instead, the reverse functions T(p,h) and T(p,s) are used to determine T, which is then used to determine v from v(p,T) in all regions. This provides a consistent approach for all regions.
The Enthalpy-Entropy table below contains the published p(h,s) values for verification of computer programs from Table 3 (p.6) and Table 9 (p.10) of IAPWS SR2-01(2014), as well as Table 5 (p.10) of IAPWS SR4-04(2014). The last three values are Tsat points from Table 29 of IAPWS SR4-04(2014).
| Region | h | s | P | error |
|---|---|---|---|---|
| [kJ/kg] | [kJ/kg/K] | [MPa] | [rel] | |
| 1 | 0.001 | 0 | 9.80098061e-04 | 1.918e-10 |
| 1 | 90 | 0 | 9.19295473e+01 | 3.631e-11 |
| 1 | 1500 | 3.4 | 5.86829442e+01 | 6.313e-12 |
| 2a | 2800 | 6.5 | 1.37101277e+00 | 1.468e-10 |
| 2a | 2800 | 9.5 | 1.87974384e-03 | 1.225e-10 |
| 2a | 4100 | 9.5 | 1.02478900e-01 | 4.457e-10 |
| 2b | 2800 | 6 | 4.79391144e+00 | 6.854e-12 |
| 2b | 3600 | 6 | 8.39551921e+01 | 5.738e-11 |
| 2b | 3600 | 7 | 7.52716144e+00 | 4.704e-11 |
| 2c | 2800 | 5.1 | 9.43920206e+01 | 2.232e-12 |
| 2c | 2800 | 5.8 | 8.41457412e+00 | 5.073e-12 |
| 2c | 3400 | 5.8 | 8.37690388e+01 | 8.322e-12 |
| 3a | 1700 | 3.8 | 2.55570325e+01 | 1.133e-10 |
| 3a | 2000 | 4.2 | 4.54087347e+01 | 4.960e-11 |
| 3a | 2100 | 4.3 | 6.07812334e+01 | 7.662e-11 |
| 3b | 2600 | 5.1 | 3.43499926e+01 | 6.694e-11 |
| 3b | 2400 | 4.7 | 6.36392489e+01 | 5.565e-11 |
| 3b | 2700 | 5 | 8.83904328e+01 | 1.360e-11 |
| ------ | -------- | ----------- | Tsat/[K] | ---------- |
| 4 | 1800 | 5.3 | 3.46847550e+02 | 2.467e-11 |
| 4 | 2400 | 6 | 4.25137331e+02 | 1.064e-10 |
| 4 | 2500 | 5.5 | 5.22557901e+02 | 8.139e-11 |
Note
Relative errors above should be on the order of 1E-10 or lower.
The RMS of all relative errors (21) is 1.247e-10
These functions for viscosity, thermal conductivity, and surface tension are not part of the IAPWS IF97 Release and its supplement documents but are part of the General and Scientific Use releases. They are simple algebraic implementations with specific instructions for Industrial Use using the IAPWS IF97 Release equations for their basic input properties at each state point with minimum error.
Pressure and Temperature points based on the tabulated computer program verification values from IAPWS R12-08, page 8, Table 4. Per guidance from IAPWS, the critical enhancement, mu2, is set to 1, resulting in slightly greater error in the lower portion of this table, very near the critical point. This function is temperature and density based. The density is determined from the IF97 formulation for the function visc_Tp(T,p). However, the direct density function, visc_TRho(T,rho) is used for the verification table below.
| T | rho | Viscocity | error |
|---|---|---|---|
| [K] | [kg/m³] | [μPa*s] | [rel] |
| 298.15 | 998 | 889.735100 | 1.684e-10 |
| 298.15 | 1200 | 1437.649467 | 2.168e-10 |
| 373.15 | 1000 | 307.883622 | 1.109e-09 |
| 433.15 | 1 | 14.538324 | 3.341e-08 |
| 433.15 | 1000 | 217.685358 | 1.218e-09 |
| 873.15 | 1 | 32.619287 | 7.977e-10 |
| 873.15 | 100 | 35.802262 | 7.768e-09 |
| 873.15 | 600 | 77.430195 | 2.935e-09 |
| 1173.15 | 1 | 44.217245 | 1.097e-08 |
| 1173.15 | 100 | 47.640433 | 1.702e-09 |
| 1173.15 | 400 | 64.154608 | 2.364e-09 |
| _________ | ___________ | __________________ | ____________ |
| 647.35 | 122 | 25.520603 | 2.898e-06 |
| 647.35 | 222 | 31.220475 | 3.737e-03 |
| 647.35 | 272 | 35.031201 | 3.304e-02 |
| 647.35 | 322 | 39.345550 | 8.417e-02 |
| 647.35 | 372 | 44.072561 | 3.536e-02 |
| 647.35 | 422 | 49.143199 | 5.928e-03 |
Note
Relative errors above should be on the order of 1E-8 or lower, except near the critical point, where they may be as high as 8.417E-2. This is due to the critical enhancement, μ2, being set to 1, per IAPWS guidance for industrial use. RMS error for first eleven points is 1.095e-08 (should be 1.095e-8 or less). RMS error for last six points is 3.97% near the critical point.
Pressure and Temperature points based on the tabulated computer program verification values from IAPWS R15-11, page 13, Tables 7,8,9. Per guidance from IAPWS, all input properties are calculated using the standard IF97 forward functions and the dimensionless isothermal compressibility, zeta, is set to a simplified correlation, resulting in slightly greater error in the lower portion of this table, very near the critical point.
This function is temperature, pressure, and density based with density determined from the IF97 density function.
| T | P | rho | Thermal Conductivity | error |
|---|---|---|---|---|
| [K] | [mPa] | [kg/m³] | [mW/m/K] | [rel] |
| 620.00 | 20 | 613.227777 | 481.4851951 | 2.084e-10 |
| 620.00 | 50 | 699.226043 | 545.0389397 | 5.151e-10 |
| 650.00 | 0.3 | 1.00452141 | 52.2311024 | 6.786e-10 |
| 800.00 | 50 | 218.030012 | 177.7099135 | 2.626e-09 |
| 647.35 | 21.98406271 | 222 | 366.8794110 | 2.820e-09 |
| 647.35 | 22.13216002 | 322 | 1241.8241478 | 1.740e-09 |
| ______ | ____________ | ___________ | ______________ | ____________ |
| 647.35 | 0.297422657 | 1 | 51.929893 | 4.876e-09 |
| 647.35 | 19.45771946 | 122 | 130.893566 | 2.239e-04 |
| 647.35 | 21.98406271 | 222 | 366.879408 | 2.469e-03 |
| 647.35 | 22.11526557 | 272 | 696.543561 | 8.103e-02 |
| 647.35 | 22.13216002 | 322 | 1241.824260 | 1.399e-01 |
| 647.35 | 22.15298122 | 372 | 625.811973 | 3.769e-02 |
| 647.35 | 22.33268694 | 422 | 448.675629 | 4.631e-04 |
Note
Relative errors above should be on the order of 1E-9 or lower, except near the critical point, where they may be as high as 1.4E-1. This is due to the critical enhancement being simplified, per IAPWS guidance for industrial use. RMS error for first six points is 1.763e-09 (should be 1.763e-9 or less). RMS error for last seven points is 6.27% near the critical point.
Temperature points based on the tabulated computer program verification values from IAPWS R1-76(2014), pages 4-5, Table 1.
| T | sigma | error |
|---|---|---|
| [K] | [mN/m] | [rel] |
| 0.01 | 75.65 | 8.291e-05 |
| 5 | 74.94 | 2.287e-05 |
| 10 | 74.22 | 1.207e-04 |
| 15 | 73.49 | 5.710e-05 |
| 20 | 72.74 | 5.306e-05 |
| 25 | 71.97 | 1.083e-04 |
| 30 | 71.19 | 5.831e-05 |
| 35 | 70.40 | 1.117e-04 |
| 40 | 69.60 | 9.071e-05 |
| 45 | 68.78 | 4.583e-05 |
| 50 | 67.94 | 2.047e-04 |
| 55 | 67.10 | 1.141e-04 |
| 60 | 66.24 | 2.623e-05 |
| 65 | 65.37 | 9.038e-05 |
| 70 | 64.48 | 1.670e-04 |
| 75 | 63.58 | 2.048e-04 |
| 80 | 62.67 | 1.140e-04 |
| 85 | 61.75 | 1.544e-04 |
| 90 | 60.82 | 6.522e-05 |
| 95 | 59.87 | 1.709e-04 |
| 100 | 58.91 | 1.380e-04 |
| 105 | 57.94 | 1.287e-04 |
| 110 | 56.96 | 1.404e-04 |
| 115 | 55.97 | 1.703e-04 |
| 120 | 54.97 | 3.348e-05 |
| 125 | 53.96 | 8.697e-05 |
| 130 | 52.93 | 1.484e-04 |
| 135 | 51.90 | 2.086e-05 |
| 140 | 50.86 | 8.123e-05 |
| 145 | 49.80 | 1.354e-04 |
| 150 | 48.74 | 1.776e-04 |
| 155 | 47.67 | 8.231e-06 |
| 160 | 46.59 | 2.295e-04 |
| 165 | 45.50 | 2.753e-04 |
| 170 | 44.41 | 1.393e-04 |
| 175 | 43.30 | 4.581e-05 |
| 180 | 42.19 | 5.573e-06 |
| 185 | 41.07 | 3.086e-05 |
| 190 | 39.95 | 1.146e-04 |
| 195 | 38.81 | 1.791e-04 |
| 200 | 37.67 | 1.456e-04 |
| 205 | 36.53 | 2.682e-04 |
| 210 | 35.38 | 5.508e-04 |
| 215 | 34.23 | 4.137e-04 |
| 220 | 33.07 | 7.063e-04 |
| 225 | 31.90 | 5.221e-04 |
| 230 | 30.74 | 7.662e-04 |
| 235 | 29.57 | 4.595e-04 |
| 240 | 28.39 | 2.186e-04 |
| 245 | 27.22 | 3.200e-05 |
| 250 | 26.04 | 2.686e-04 |
| 255 | 24.87 | 2.426e-04 |
| 260 | 23.69 | 1.220e-03 |
| 265 | 22.51 | 2.324e-03 |
| 270 | 21.34 | 2.197e-03 |
| 275 | 20.16 | 1.161e-03 |
| 280 | 18.99 | 3.323e-03 |
| 285 | 17.83 | 3.729e-03 |
| 290 | 16.66 | 3.878e-03 |
| 295 | 15.51 | 3.782e-03 |
| 300 | 14.36 | 4.169e-03 |
| 305 | 13.22 | 2.976e-03 |
| 310 | 12.09 | 4.049e-03 |
| 315 | 10.97 | 4.564e-03 |
| 320 | 9.86 | 5.541e-03 |
| 325 | 8.77 | 5.091e-03 |
| 330 | 7.70 | 5.561e-03 |
| 335 | 6.65 | 6.318e-03 |
| 340 | 5.63 | 6.347e-03 |
| 345 | 4.63 | 6.120e-03 |
| 350 | 3.67 | 6.978e-03 |
| 355 | 2.74 | 1.746e-03 |
| 360 | 1.88 | 6.782e-03 |
| 365 | 1.08 | 3.567e-02 |
| 370 | 0.39 | 1.373e-01 |
Note
Relative errors above should be on the order of 1E-3 or lower below 260 °C and
on the order of 1E-2 or lower above 260 °C.
The RMS of all relative errors (75) is 1.655e-02