Humid Air / Psychrometry

Psychrometry (humid air) studies the thermodynamic and transport properties of air–water vapor mixtures. Important state variables are dry-bulb temperature (T, °C), partial pressure of water vapor (pv, kPa), relative humidity (RH, fraction or %), humidity ratio (ω, kg water vapor per kg dry air), dew point temperature (Td, °C), wet-bulb temperature (Twb, °C), and moist-air enthalpy (h, kJ per kg dry air). At typical atmospheric conditions the ideal-gas approximation applies separately to dry air and water vapor. Processes include sensible heating/cooling (ω constant), humidification/dehumidification (ω changes), adiabatic saturation (evaporative cooling) and mixing of streams at constant pressure. Standard reference atmospheric pressure is 101.325 kPa unless otherwise stated.

Governing FormulaUseful relations (T in °C, pressures in kPa, energies in kJ/kg dry air): - Saturation vapor pressure (Magnus–Tetens approximation): es(T) = 0.61078 * exp(17.27*T/(T + 237.3)) (kPa) - Partial pressure of vapor: pv = RH * es(T) (RH as fraction) - Humidity ratio (mass of water vapor per mass dry air): ω = 0.622 * pv / (p - pv) (kg water/kg dry air), where p is total pressure (kPa) - Inverse Magnus (dew point from pv): Td = 237.3 * ln(pv/0.61078) / (17.27 - ln(pv/0.61078)) (°C) - Specific enthalpy of moist air (per kg dry air, approximate): h = cp_da * T + ω * (hg0 + cp_v * T) with cp_da = 1.005 kJ·kg^-1·K^-1, cp_v = 1.86 kJ·kg^-1·K^-1, hg0 (approx latent heat at 0 °C) = 2501 kJ/kg. Hence: h ≈ 1.005*T + ω*(2501 + 1.86*T) (kJ/kg dry air) - Relation for solving mixture temperature: For given mixed h and ω, T = (h - ω*2501) / (1.005 + ω*1.86) (°C) - Note/assumptions: ideal-gas behavior for components, standard cp and latent heat constants above, pressure p = 101.325 kPa unless specified otherwise.

Knowledge Check

10 Questions

1.Which expression correctly gives the humidity ratio ω (kg water vapor per kg dry air) in terms of vapor partial pressure pv (kPa) and total pressure p (kPa)? Assume ideal-gas behavior.

2.Using the Magnus formula es(T) = 0.61078·exp(17.27·T/(T+237.3)), what is the saturation vapor pressure es at T = 20 °C (kPa)?

3.Air at p = 101.325 kPa has dry-bulb temperature 25 °C and relative humidity 40%. Using the Magnus relation and ω = 0.622·pv/(p - pv), what is the humidity ratio ω (kg water/kg dry air)?

4.At T = 30 °C and RH = 60% (p = 101.325 kPa), what is the dew point temperature Td (°C)? Use Magnus relations and give answer to two decimals.

5.Compute the moist-air enthalpy h (kJ per kg dry air) for air at T = 20 °C and RH = 50% (p = 101.325 kPa). Use h ≈ 1.005·T + ω·(2501 + 1.86·T) with Magnus for ω.

6.If water is evaporated into an air stream at constant dry-bulb temperature (T constant) and constant pressure, which of the following is true (before reaching saturation)?

7.Two moist-air streams (same pressure) are mixed adiabatically. Stream A: 1 kg dry air at T = 30 °C with ω = 0.010 kg/kg. Stream B: 2 kg dry air at T = 10 °C with ω = 0.004 kg/kg. Using h ≈ 1.005·T + ω·(2501 + 1.86·T), what is the temperature (°C) of the mixed air (per kg dry air basis)?

8.Air at 40 °C is saturated (RH = 100%) at p = 101.325 kPa. What is the approximate humidity ratio ω (kg/kg dry air)?

9.Which statement about wet-bulb temperature Twb and adiabatic saturation temperature Tas is correct for unsaturated air at common pressures?

10.How much liquid water (g) must be evaporated into 1.00 kg dry air at T = 20 °C to raise RH from 30% to 70% (p = 101.325 kPa)? Use Magnus and ω = 0.622·pv/(p - pv).