Moist air enters an adiabatic humidifier at state 1 [21.1 °C (70 F), 1 atm, 10% relative humidity] with a volumetric flow rate of 500 ft³/min. The air leaves the humidifier at state 2 [23.9 °C (75 F), 1 atm, 70% relative humidity]. The change in the condition of the moist air is brought about by the injection of steam at state 3 from a boiler, as shown in the diagram. The boiler is supplied with 23.3° C (74 F) water at state 4. An adiabatic valve between the boiler and the humidifier causes the steam pressure to drop from boiler pressure to the humidifier pressure of 1 atm.

A. Determine the mass flow rate (kg/min) of the water at state 4.

B. Determine the heat-transfer rate to the boiler (kW).

C. Determine the pressure (kPa) in the boiler.

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Humidifier 3 Valve Boiler 2