An airconditioning system consists of a heating section foll

An air-conditioning system consists of a heating section followed by a humidifier operating at a constant pressure of 20 psia. Atmospheric air enters the heating section at 50 degree F and 78% relative humidity at a flow rate of 1800 ft^3/min and is heated to a desired temperature by a 20 kW electric heater before it enters the humidifier section. Humidification is achieved by injecting saturated water vapor at 220 degree F, at a rate of 0.35 Ibm/min, into the airflow. Determine the Temperature at the end of the heating process (before humidification) Temperature and specific humidity of the air exiting the air-conditioning system. (Do not use the Psychrometric chart for the solution; 1 kW=0.9478 Btu/sec)

Solution

at 50 F and 78 % RH

Enthalpy = 18.43 BTU /lb

specific volume = 12.9665 ft^3/lb

Enthalpy after heat injection

Q = 20 kW   = 18.956 BTU/s

Flow rate = 1800 ft^3/min   = 30 ft^3/s

mass flow rate = flow rate / specific volume   = 30 / 12.9665   = 2.313654 lb/s

final enthalpy after heating   = 18.43 + 18.956 / 2.313654   = 26.6231 BTU/lb

a) Temperature after heating ( h = 26.6231 BTU/lb and 78 % RH ) = 64.75 F

b) enthalpy of water vapor   = 1150 BTU/lb

     mass flow rate of vapor = (0.35 /60) = 0.005833 lb/s

     Enthalpy after mixing   = 0.00583 * 1150 + 2.313654 * 26.6231 = 68.3046 BTU/s

     Temperature at exit   = 98.15 F   and RH = 100 %

     humidity ratio = 0.0405 lb/lb