✓ Verified Accuracy

Calculations Compliant with ASHRAE Fundamentals 2021

The psychrometric core implements the equations from Chapter 1 of the ASHRAE Handbook — Fundamentals including real-gas correction (enhancement factor). Every quantity has been numerically compared with ASHRAE reference tables across the full HVAC temperature range.

0.02 %
Saturation pressure
max. deviation p_ws in HVAC range
0.08 %
Specific humidity
max. deviation Ws up to +50 °C
0.10 kJ/kg
Enthalpy
max. absolute deviation hs up to +50 °C
0.10 %
Specific volume
max. deviation vs across full range
⚡

Key to Accuracy: Enhancement Factor

The standard formula for specific humidity assumes ideal gas behaviour: W = ε · p_ws / (p − p_ws). In a real atmosphere, water vapour mixed with dry air exhibits cross-species interactions (cross-virial coefficient Baw), which effectively increase the partial pressure of vapour. The application corrects for this physical reality with the enhancement factor f (Buck 1981 / WMO No. 8 / ASHRAE Eq. 18):

Over liquid water (t ≥ 0 °C)

f = 1.0016 + 3.15×10⁻⁶·phPa − 0.074/phPa

Over ice (t < 0 °C)

f = 1.0003 + 4.18×10⁻⁶·phPa

📈 Impact of enhancement factor on accuracy (−40…+50 °C, p = 101.325 kPa)

Quantity Without correction With factor f Improvement
p_ws ±0.04 % ±0.02 % unchanged
Ws (specific humidity) up to −0.62 % ±0.08 % 8×
hs (enthalpy) up to −0.40 % ±0.11 % 4×
hs abs. up to −1.1 kJ/kg <0.1 kJ/kg 11×
vs (specific volume) ±0.13 % ±0.10 % minor

Calculation Methodology

In ASHRAE mode the application calculates saturation pressure using the Hyland–Wexler correlation (equations 5 and 6) with original coefficients C1–C13. All other quantities are derived from it:

  • Specific humidity W = ε · f · p_ws / (p − f · p_ws) (eq. 20 + enhancement factor, ε = 0.621945)
  • Enthalpy h = 1.006·t + W·(2501 + 1.86·t) (eq. 30)
  • Specific volume v = 0.287042·T·(1 + 1.607858·W) / p (eq. 26)

Reference values are ASHRAE Table 2 (properties of saturated moist air, real-gas model LibHuAirProp / RP-1485) and Table 3 (saturation pressure). Comparison performed at standard pressure 101.325 kPa.

The residual deviation of specific humidity ±0.08 % is the fundamental limit of the perfect-gas model and corresponds to the accuracy of ASHRAE equations 20 and 26 relative to a full real-gas calculation (LibHuAirProp).

Detailed Deviation Tables

Saturation pressure pws [kPa]

Hyland–Wexler correlation. Max. deviation ±0.02 % in HVAC range.

t [°C]AppASHRAEDeviation
-20 0.10326 0.10324 +0.020 %
0 0.61121 0.61121 +0.000 %
10 1.22799 1.22820 −0.017 %
20 2.33880 2.33920 −0.017 %
30 4.24603 4.24670 −0.016 %
40 7.38346 7.38440 −0.013 %
50 12.34985 12.35100 −0.009 %

Saturation specific humidity Ws [g/kg]

With enhancement factor. Max. deviation ±0.08 % — 8× improvement over uncorrected version.

t [°C]AppASHRAEDeviation
-20 0.637 0.637 +0.008 %
0 3.792 3.790 +0.063 %
10 7.666 7.663 +0.050 %
20 14.766 14.761 +0.034 %
30 27.337 27.333 +0.013 %
40 49.131 49.145 −0.028 %
50 86.791 86.863 −0.083 %

Saturation air enthalpy hs [kJ/kg]

Max. absolute deviation 0.096 kJ/kg up to +50 °C — 11× improvement over uncorrected version.

t [°C]AppASHRAEΔ [kJ/kg]Deviation
-20 −18.550 −18.542 −0.008 +0.041 %
0 9.485 9.474 +0.010 +0.109 %
10 29.377 29.354 +0.023 +0.077 %
20 57.599 57.558 +0.041 +0.071 %
30 100.074 100.010 +0.064 +0.064 %
40 166.773 166.680 +0.093 +0.056 %
50 275.436 275.340 +0.096 +0.035 %

Saturation air specific volume vs [m³/kg]

Max. deviation 0.10 % — residual error of the perfect-gas model.

t [°C]AppASHRAEDeviation
-20 0.71788 0.71720 +0.095 %
0 0.77852 0.77800 +0.067 %
10 0.81202 0.81160 +0.052 %
20 0.85018 0.84980 +0.044 %
30 0.89654 0.89610 +0.049 %
40 0.95720 0.95670 +0.052 %
50 1.04319 1.04250 +0.067 %

Conclusion

Across the full range relevant for HVAC (−40 to +50 °C), the application results are in excellent agreement with ASHRAE: saturation pressure within 0.02 %, specific humidity within 0.08 %, enthalpy within 0.10 kJ/kg, and specific volume within 0.10 %. These deviations are well below the accuracy of typical measuring instruments (humidity sensors ±2–5 %, thermometers ±0.1–0.5 °C).

References: ASHRAE Handbook — Fundamentals (2021), Chapter 1 · Hyland & Wexler (1983) · Buck (1981) · WMO No. 8 CIMO Guide (2018).

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