Psychrometrics

Why it matters

Psychrometrics is essential in designing and analyzing HVAC (Heating, Ventilation, and Air Conditioning) systems, which are crucial for maintaining indoor air quality and comfort. Understanding psychrometric principles helps engineers optimize energy efficiency and ensure proper environmental control in various applications, from residential buildings to industrial processes.

Key ideas

• Moist Air: A mixture of dry air and water vapor. The properties of moist air are crucial for understanding psychrometrics.
• Dry Bulb Temperature (DBT): The temperature of air measured by a regular thermometer, expressed in degrees Celsius (°C).
• Wet Bulb Temperature (WBT): The temperature indicated by a thermometer covered with a water-soaked cloth over which air is passed, expressed in degrees Celsius (°C).
• Dew Point Temperature: The temperature at which air becomes saturated with moisture and dew begins to form, expressed in degrees Celsius (°C).
• Relative Humidity (RH): For an ideal moist-air approximation, water-vapor partial pressure divided by saturation vapor pressure at the dry-bulb temperature, expressed as a percentage.
• Humidity Ratio: The mass of water vapor per unit mass of dry air, expressed in kg/kg of dry air.
• Enthalpy of Moist Air: A property expressed here per kg of dry air, relative to a chosen reference state.
• Psychrometric Chart: A graphical representation of the physical and thermal properties of moist air.

Formulas

• RH = (Pw / Pws) * 100
  • RH: Relative Humidity (%), Pw: Partial pressure of water vapor (Pa), Pws: Saturation pressure of water vapor at the same temperature (Pa).
• h = ha + ω * hg
  • h: Enthalpy of moist air (kJ/kg), ha: Enthalpy of dry air (kJ/kg), ω: Humidity ratio (kg/kg), hg: Enthalpy of water vapor (kJ/kg).
• ω = 0.622 * (Pw / (P - Pw))
  • ω: Humidity ratio (kg/kg), Pw: Partial pressure of water vapor (Pa), P: Atmospheric pressure (Pa).

Definitions and basis

Humidity ratio ω = m_vapor/m_dry_air differs from specific humidity q = m_vapor/(m_vapor+m_dry_air) = ω/(1+ω). Psychrometric enthalpy h = h_a + ωh_g is per kg of dry air. Saturation pressure for relative humidity must be evaluated at dry-bulb temperature, not wet-bulb temperature. A psychrometric chart is prepared for a specified total pressure.

Worked example

Moist air has dry-bulb temperature 30°C, total pressure P = 101.3 kPa and measured vapor partial pressure P_w = 2.50 kPa. For this exercise use the supplied saturation pressure P_ws(30°C) = 4.246 kPa.

RH = (2.50/4.246)100 = 58.88%. ω = 0.622(2.50)/(101.3-2.50) = 0.015739 kg vapor/kg dry air. q = ω/(1+ω) = 0.015495 kg vapor/kg moist air.

These are three different quantities. If wet-bulb temperature is given instead of P_w, use a validated psychrometric relation or chart at the correct pressure and distinguish a measured psychrometer temperature from the thermodynamic wet-bulb model.

Common processes

Sensible heating without adding/removing vapor leaves ω unchanged but generally lowers RH. Cooling at constant ω reaches the dew point when P_ws(T_dp) = P_w; further cooling can condense water. Adiabatic humidification often follows approximately constant moist-air enthalpy under the usual simplified assumptions.

Common mistakes

• Confusing dry bulb and wet bulb temperatures.
• Incorrectly reading values from psychrometric charts.
• Neglecting the effect of atmospheric pressure on calculations.

For GATE ME

Questions often involve calculating properties like relative humidity, humidity ratio, and enthalpy using given temperatures and pressures. Practice using psychrometric charts and understanding the relationships between different properties of moist air.

Quick check

1. What is the significance of the dew point temperature?
2. How is humidity ratio different from relative humidity?
3. What does a psychrometric chart represent?

Answers: 1. It indicates the temperature at which air becomes saturated. 2. Humidity ratio is the mass of water vapor per unit mass of dry air, while relative humidity is a percentage of current to maximum possible humidity. 3. It represents the properties of moist air.