Psychrometrics Calculator — ThermoFluidCalc

Moist Air State Relations

Moist air thermodynamic properties are fully defined by barometric pressure and any two independent parameters. The chart visually relates sensible, latent, and total energy bounds.

• Dry-Bulb ($T_{db}$): Sensible temperature representing the thermal state of the mixture.
• Wet-Bulb ($T_{wb}$): Dynamic thermodynamic equilibrium under adiabatic saturation.
• Dew-Point ($T_{dp}$): The limit temperature where partial vapor pressure equals saturation pressure.
• Humidity Ratio ($\omega$): The absolute moisture content by mass.

📝 Configuration

Input Combination:

Inlet Conditions

Dry-Bulb Temperature ($T_{db}$) [°C]:

Barometric Pressure ($P$) [kPa]:

Relative Humidity ($RH$) [%]:

Quick Presets:

Thermodynamic Definitions:
• Relative Humidity: $RH = P_v / P_{sat}(T)$
• Saturation Vapor Pressure: Buck Formulation (kPa)
• Specific Enthalpy: $h = 1.006T + \omega(2501 + 1.86T)$ (kJ/kg)
• Specific Volume: $v = R_{air}(T + 273.15)/(P - P_v)$ (m³/kg)
• Humidity Ratio: $\omega = 0.62198 P_v/(P - P_v)$ (kg/kg)

Note: Wet-bulb temperature is solved iteratively using the adiabatic saturation equation to within 10⁻⁵ °C precision.

📊 Results & Visualization

Configure inputs and click Solve Moist Air Properties to view results.

📘 Calculation Methodology

Mathematical Model & Theory

Psychrometrics deals with thermodynamic properties of moist air. Key definitions include relative humidity ($RH$), humidity ratio (absolute moisture content $\omega$), and dew-point temperature. Under the assumption of ideal gas behavior for water vapor and dry air components:

$$\omega = 0.62198 \frac{P_v}{P - P_v}, \quad RH = \frac{P_v}{P_{sat}(T)}$$ $$h = 1.006 T + \omega (2501 + 1.86 T) \quad \text{[kJ/kg dry air]}$$

Saturation vapor pressure ($P_{sat}$) is computed using the Buck Formulation. Wet-bulb temperature ($T_{wb}$) is solved iteratively based on the adiabatic saturation relation:

$$\omega = \frac{(2501 - 2.381 T_{wb}) \omega_{sat}(T_{wb}) - 1.006(T - T_{wb})}{2501 + 1.86 T - 4.186 T_{wb}}$$

Assumptions & Limits

Dry air and water vapor behave as ideal gases.
Total mixture pressure is barometric pressure (Dalton's Law of Partial Pressures).
Temperature range limited to $-30^\circ\text{C} \le T_{db} \le 60^\circ\text{C}$ for HVAC applicability.

Academic References

ASHRAE Handbook - Fundamentals: Chapter 1: Psychrometrics (2021).
Buck, A. L.: "New Equations for Computing Vapor Pressure and Enhancement Factor", Journal of Applied Meteorology (1981).

Worked Engineering Example

Problem Statement:
Air at 25°C and 101.325 kPa has a relative humidity $RH = 50\%$. Find the humidity ratio $\omega$ and specific enthalpy $h$. ($P_{sat}$ at 25°C is 3.169 kPa).

Step-by-step Solution:
1. Calculate vapor pressure $P_v$:
$$P_v = RH \times P_{sat} = 0.50 \times 3.169 = 1.5845 \text{ kPa}$$ 2. Calculate humidity ratio $\omega$:
$$\omega = 0.62198 \times \frac{1.5845}{101.325 - 1.5845} = 0.00987 \text{ kg water / kg dry air} = 9.87 \text{ g/kg}$$ 3. Calculate specific enthalpy $h$:
$$h = 1.006 \times 25 + 0.00987 \times (2501 + 1.86 \times 25) = 25.15 + 25.14 = 50.29 \text{ kJ/kg dry air}$$
Final Result:
Humidity ratio is 9.87 g/kg and enthalpy is 50.29 kJ/kg.