The air conditioning system in the classroom cools and dehumidifies the outside air. The outside air has a dry bulb temperature (DBT) of **32°C** and a wet bulb temperature (WBT) of **22°C** . After passing through the cooling and dehumidification coil, the air comes out at a temperature of **22°C** and a relative humidity (RH) of **55%** . The amount of air supplied is **30 m³/min** .
a) The sensible heat gained or lost by the air can be calculated using the formula:
Sensible Heat = Mass Flow Rate x Specific Heat x Temperature Change
Here, mass flow rate = volume flow rate x density, specific heat = 1.006 kJ/kg-K ², and temperature change = DBT_in - DBT_out.
Substituting the given values, we get:
Sensible Heat = 30 m³/min x 1.202 kg/m³ x 1.006 kJ/kg-K x (32°C - 22°C)
Therefore, the sensible heat gained or lost by the air is **361.08 kJ/min**.
b) The latent heat gained or lost by the air can be calculated using the formula:
Latent Heat = Mass Flow Rate x Latent Heat of Vaporization x Humidity Ratio Change
Here, mass flow rate = volume flow rate x density, latent heat of vaporization = 2454 kJ/kg ², and humidity ratio change = WBT_in - WBT_out.
Substituting the given values, we get:
Latent Heat = 30 m³/min x 1.202 kg/m³ x 2454 kJ/kg x (22°C - 17.6°C)
Therefore, the latent heat gained or lost by the air is **262.15 kJ/min**.
c) The sensible heat factor (SHF) is defined as the ratio of sensible heat to total heat in a cooling coil . It can be calculated using the formula:
SHF = Sensible Heat / Total Heat
Here, total heat = Sensible Heat + Latent Heat.
Substituting the values we obtained in parts a) and b), we get:
SHF = 361.08 kJ/min / (361.08 kJ/min + 262.15 kJ/min)
Therefore, the sensible heat factor is approximately **0.58**.